If vector A = 6i - 2j + 3k, determine
(a) A vector in the same direction as A with magnitude 2A
(b) A unit vector in the direction of A
(c) a vector opposite to A with magnitude of 4 m​

Answers

Answer 1

Answer:

(a) [tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]

(b) [tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]

(c) [tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]

Explanation:

Vectors

Given a vector

[tex]\vec A=6\hat i-2\hat j+3\hat k[/tex]

We must determine the following:

a) A vector in the same direction as A with double magnitude 2A.

If the vector goes in the same direction but has a different magnitude, we only need to multiply each component by a common factor, in this case, by 2. Thus, the required vector is:

[tex]2\vec A=12\hat i-4\hat j+6\hat k[/tex]

b) A unit vector in the same direction of A.

The unit vector needs to compute the magnitude of the vector:

[tex]\mid A\mid=\sqrt{6^2+2^2+3^2}[/tex]

[tex]\mid A\mid=\sqrt{36+4+9}=\sqrt{49}=7[/tex]

[tex]\mid A\mid=7[/tex]

The unit vector is:

[tex]\displaystyle \vec{U_A}=\frac{\vec A}{\mid \vec A\mid}[/tex]

[tex]\displaystyle \vec{U_A}=\frac{12\hat i-4\hat j+6\hat k}{7}[/tex]

[tex]\displaystyle \vec{U_A}=12/7\hat i-4/7\hat j+6/7\hat k[/tex]

c) A vector opposite to A with magnitude 4 m. We assume the original vector is also expressed in m.

The opposite vector to A is obtained simply by multiplying the unit vector by -1. To make its magnitude equal to 4, also multiply by 4. In all, we multiply the unit vector by -4:

[tex]-4\vec{U_A}=-4(12/7\hat i-4/7\hat j+6/7\hat k)[/tex]

[tex]-4\vec{U_A}=-48/7\hat i+16/7\hat j-24/7\hat k[/tex]


Related Questions

what phase changes take place when you are adding energy to the substance

Answers

Answer:

During a phase change, a substance undergoes transition to a higher energy state when heat is added, or to a lower energy state when heat is removed. Heat is added to a substance during melting and vaporization. Latent heat is released by a substance during condensation and freezing. Explanation:

A race car accelerates from rest to a velocity of +90 m/s over a distance of 423m. Determine the acceleration of the race car.

Answers

Answer:

9.57m/s²

Explanation:

Given parameters:

Initial velocity  = 0m/s

Final velocity  = 90m/s

Distance  = 423m

Unknown:

Acceleration of the race car  = ?

Solution:

To solve this problem, we should apply one of the appropriate motion equations;

      V²  = U²   + 2as

Where V is the final velocity

           U is the initial velocity

           a is the acceleration

           s is the distance

  90²  = 0²  + 2 x a x 423

  8100 = 846a

      a  = 9.57m/s²

Why is it better to use the metric system, rather than the English system, in scientific measurement?

A. The English system uses one unit for each category of measurement.
B. The metric system uses one unit for each category of measurement.
C. The English system uses consistent fractions that are multiples of 10.
D. The metric system utilizes a variety of number conversions.

Answers

A. The English system uses one unit for each category of measurement.

Answer:

A

Explanation:

What is your role in motivating yourself?

Answers

i typically focus on motivating others.. i wanna be a motivational speaker someday. tbh if anyone needs anyone to talk to id be happy to listen and i would give the best advice i can. heres my discord: ionknow22#2868

An increase in temperature the kinetic energy and average speed of the gas particles. As a result, the pressure on the walls of the container . Answer Bank What temperature must a gas, initially at 10 ∘C, be brought to for the pressure to triple?

Answers

Answer:

a

The pressure will increase

b

[tex]T_2 =  576^oC[/tex]

Explanation:

From the ideal gas law we have that

     [tex]PV  =  nRT[/tex]

We see that the temperature varies directly with the pressure so if there is an increase in temperature that pressure will increase

   The initial  temperature is [tex]T_i  =  10^oC = 10 + 273 =  283 \  K [/tex]

The objective of this solution is to obtain the temperature of the gas where the pressure is tripled

Now from the above equation given that nR and V  are constant  we have that

    [tex]\frac{P}{T}  =  constant[/tex]

=>  [tex]\frac{P_1}{T_1}  =\frac{P_2}{T_2}[/tex]

Let assume the initial  pressure is [tex]P_1 =  1 Pa[/tex]

So tripling it will result  to the pressure being [tex]P_2 =  3 Pa[/tex]

So

     [tex]\frac{1}{283}  =\frac{3}{T_2}[/tex]  

=>   [tex]T_2  =  3 *  283[/tex]

=>    [tex]T_2  =  3 *  283[/tex]

=>    [tex]T_2  = 849 \ K [/tex]

Converting back to [tex]^oC[/tex]

   [tex]T_2  =  849 -  273[/tex]

=>  [tex]T_2 =  576^oC[/tex]

What do mammoths and tigers need energy for

Answers

Muscles
.............

An object at rest starts accelerating.
If it travels 20 meters to end up going 10 m/s.
what was its acceleration?
Variables:
Equation and Solve:

Answers

Answer:

We are given:

initial velocity (u) = 0 m/s

final velocity (v) = 10 m/s

displacement (s) = 20 m

acceleration (a) = a m/s/s

Solving for 'a'

From the third equation of motion:

v² - u² = 2as

replacing the variables

(10)² - (0)² = 2(a)(20)

100 = 40a

a = 100 / 40

a = 2.5 m/s²

I need help please help ! For science

Answers

Answer:

1, 5, 4, 6

Explanation:

bc

What is the answer to this ?

Answers

Symbolic interactionism

Which best explains a difference between Einstein’s general theory of relativity and his special theory of relativity?


His general theory includes uniform and accelerated motion, but his special theory applies only to uniform motion.

His general theory includes uniform and accelerated motion, but his special theory applies only to accelerated motion.

His general theory applies only to accelerated motion, but his special theory includes uniform and accelerated motion.

His general theory applies only to uniform motion, but his special theory includes uniform and accelerated motion.

Answers

Answer:

His general theory includes uniform and accelerated motion, but his special theory applies only to uniform motion.

Explanation:

According to Einstein's 1915 general theory of relativity, the force of gravity arises from the curvature of space and time.

According to theory of special relativity:

1. The laws of physics are the same for all non-accelerating observers

2. The speed of light in a vacuum was independent of the motion of all observers.

His general theory includes uniform and accelerated motion, but his special theory applies only to uniform motion.

Answer:

for those who dont like to read

the answer is A.

hope i helped

Explanation:

PLEASE HELP EASY MULTIPLE CHOICE!!!!!!!!!!!

Answers

Answer:

options C is correct

Explanation:

asking questions is super in this education life

Answer:

option c should be the answer

An object is accelerating if it is moving?


Answers

9514 1404 393

Answer:

  Not Necessarily

Explanation:

If the object is changing speed or direction, then it is accelerating. If it is maintaining the same speed and direction, it is not accelerating.

anyone to assist me on it ...especial page7 and 8

Answers

Answer:

i needed points it was an emergency sorry

Explanation:

The smokestack of a stationary toy tra in consists

of a vertical spring gun chat shoots a steel ball a meter

or so straight into the air-----so straight that the ball

always falls back into the smokescack. Suppose the

train moves at constant speed along the straight track. Do you think the ball will still return to the smoke-

stack if shot from the moving train? What if the train

gains speed along the straight track? What if it moves at a constant speed on a circular track? Discuss why your answers differ,

Answers

Answer:

i)The ball shot out of the smokestack of a train moving in a straight line at constant speed will fall back into the smokestack

ii)The ball shot out of the smokestack of a train moving in a straight track ( gaining speed ) will fall behind the smoke stack

iii) The ball shot out of the smokestack of a train moving in a circular track at constant speed will fall away from the smokestack in a direction that is away from the middle of the circular track

Explanation:

The ball shot out of the smokestack of a train moving in a straight line at constant speed will fall back into the smokestack

The ball shot out of the smokestack of a train moving in a straight track ( gaining speed ) will fall behind the smoke stack

The ball shot out of the smokestack of a train moving in a circular track at constant speed will fall away from the smokestack in a direction that is away from the middle of the circular track

A car which is traveling at a velocity of 15 m/s undergoes an acceleration of 6.5 m/s2 over a distance of 340 m. How fast is it going after that acceleration?

Answers

Answer:68.15m/s

Explanation:

Given:

v₁=15m/s

a=6.5m/s²

v₁=?

x=340m

Formula:

v₁²=v₁²+2a (x)

Set up:

=[tex]\sqrt{15m/s} ^{2} +2(6.5m/s^2)(340m)[/tex]

Solution:68.15m/s

Design a tension member and slip-critical splice to carry a factored load of 500 kips. Please use a wide-flange section for the tension member. Please use A572 Gr. 50 steel plates for the splice plates. Please use Group B, A490 bolts for the splice connection. The splice connection should be slip-critical, and have adequate strength after slip occurs as well. Please make any other assumptions you need in order to complete the problem. Provide detailed sketches and drawings for your design.

Answers

Answer:

Kindly check the explanation section.

Explanation:

For the design we are asked for in this question/problem there is the need for us to calculate or determine the strength in fracture and that of the yield. Also, we need to calculate for the block shear strength.

From the question, we have that the factored load = 500kips. Also, note that the tension splice must not slip.

Also, the shear force are resisted by friction, that is to say shear resistance = 1.13 × Tb × Ns.

Assuming our db = 3/4 inches, then the slip critical resistance to shear service load = 18ksi(refer to AISC manual for the table).

If db = 7/8 inches, then the shear force resistance for n bolt = 10.2kips, n > 49.6.

The yielding strength = 0.9 × Aj × Fhb= 736 kips > 500

The fracture strength = .75 × Ah × Fhb = 309 kips.

The bearing strength of 7/8 inches bolt at the edge hole and other holes = 46 kips and 102 kips.

Someone help me I’ll give brainliest

Answers

Answer:

2.83 m/s

Explanation:

you have the right answer

Which of the following is the closest to the scientific fact
A. A hypothesis
B. A theory
C. An opinion
D. A prediction

Answers

B - A theory seems to be the closest

A theory is the closest to a scientific fact (Option B).

A scientific theory is a well-sustained scientific idea that has been verified using the scientific method.

A scientific theory can be refuted by the emergence of new lines of evidence against some aspect of this scientific statement.

A hypothesis is a given explanation about a question that emerged by observing the natural world.

In conclusion, a theory is the closest to a scientific fact (Option B).

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Hi, Please help.. I have assignments due tonight and I need someone to help me when a question I have generally..

Okay so if Density = Mass divided by Volume and I put that information into a calculator it comes out as
ex. 1.938773646 how do I make it look like something like this 1.4?

Answers

Answer:

did you tried putting it in standard form

Answer:

It may help to round all of the given numbers up to at least 1 or 2 decimal points or you could round up the number you get to 1 or 2 decimal places. For example, for this question round up your answer to 1.9 or 1.94

Explanation:

hope this helps!!

Please help me with this!

Answers

hope this helps good luck

Calculate the effective charges on the H and F atoms of the HF molecule in units of the electronic charge, e.

Answers

Answer:

Explanation:

Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is as seen below

HF ⇄ H⁺ + F⁻

There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ coloumbs.

The required value of effective charge on HF molecule, due to H and F is  1.602 × 10⁻¹⁹ Coulombs.

The given problem is based on the concept of effective charges. The net positive charge carried out by the electrons of atomic species, after forming a polyelectronic atom  is known as Effective charge.

As per the given problem, the Hydrogen fluoride (HF) is an ionic/electrovalent compound that dissociates into ions when dissolved in water. It's dissociation is given as,

HF ⇄ H⁺ + F⁻

There is a transfer of electron from the hydrogen atom which produces the hydrogen ion (H⁺), while the fluorine atom receives the donated ion to become negatively charged (F⁻). The amount of charge in one electron is generally given as 1.602 × 10⁻¹⁹ Coulombs.

Thus, we can conclude that the required value of effective charge on HF molecule, due to H and F is 1.602 × 10⁻¹⁹ Coulombs.

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A designer is creating an obstacle for an obstacle course where a person starts on a moveable platform of height H from the ground. The person grabs a rope of length L and swings downward. At the instant the rope is vertical, the person lets go of the rope and attempts to reach the far side of a water-filled moat. The left side of the moat is directly below the position where the person will let go of the rope. The designer runs several tests in which the rope has different lengths and moves the platform such that the rope is always initially horizontal. The designer notices that the person cannot land on the other side if the length L is very short. The designer also notices that the person also cannot land on the other side if the length L is very close to the height H.

Assume the size of the person is much smaller than the lengths L and H. Let D represent the horizontal distance from below the release point to where the person lands.

Required:
a. Why does the person land in the moat if the rope's length is very short?
b. Why does the person land in the moat if the length is nearly the same as the height of the platform?

Answers

Answer:

* when L → H    chord too long

in this case we see that the speed to cross the well grows a lot (it goes towards infinity) therefore we do not have enough speed in the movement to cross

* when L → 0 very short string

         the speed of the platform is very small, so we do not have the minimum required value

        vox = √ (g / (2 (H)) D

Explanation:

For this exercise we are going to solve it using conservation of energy to find the velocity of the body and the launch of projectiles to find the velocity to cross the well.

Let's start with the projectile launch

as the body leaves the vertical its velocity must be horizontal

         x = v₀ₓ t

         y = y₀ + [tex]v_{oy}[/tex] t - ½ g t²

when reaching the ground its height of zero (y = 0) and the initial vertical velocity is zero

         t = √ 2 y₀ / g

we substitute

        x = vox √2y₀ / g

        v₀ₓ = √(g / 2y₀)     x

In the exercise, it tells us that the width of the well is D (x = D) and the initial height is the height of the platform minus the length of the rope (I = H - L)

       v₀ₓ = √(g /(2 (H -L))    D

this is the minimum speed to cross the well.

Now let's use conservation of energy

starting point. On the platform

      [tex]Em_{o}[/tex] = U = m g H

final point. At the bottom of the swing

      Em_{f} = K + U = 1 / 2m v² + m g (H -L)

as there is no friction the mechanical energy is conserved

        Em_{o} = Em_{f}

       m g H = 1 / 2m v² + m g (H -L)

        v = √ (2gL)

let's write our two equations

the minimum speed to cross the well

       v₀ₓ = √ (g /(2 (H -L))    D

the speed at the bottom of the oscillatory motion

       v = √ (2g L)

we analyze the extreme cases

* when L → H    chord too long

in this case we see that the speed to cross the well grows a lot (it goes towards infinity) therefore we do not have enough speed in the movement to cross

* when L → 0 very short string

         the speed of the platform is very small, so we do not have the minimum required value

        vox = √ (g / (2 (H)) D

From this analysis we see that there is a range of lengths that allows us to have the necessary speeds to cross the well

      V₀ₓ = v

      g / (2 (H -L) D² = 2g L

       4 L (H- L) = D²

        4 H L - 4 L2 - D² = 0

        L² - H L - D² / 4 = 0

let's solve the quadratic equation

      L = [H ± √ (H2-D2)] / 2

we assume that H> D

       L = ½ H [1 + - RA (1 - (D / H) 2)]

The two values ​​of La give the range of values ​​for which the two speeds are equal

A) The person lands in the moat if the rope's length is very short because :

The speed of the platform is less than the required minimum speed

B) The person lands in the moat if the rope length is similar to the height of the platform because :

The speed required to cross the moat approaches infinity

Following the assumptions;

size of the person is much smaller than L and H

D = horizontal distance

The conditions that will cause the person to land on the moatThe person will land in the moat when the rope's length is very short because as the rope reduces in length the speed reduces as well such that the speed of the platform goes below the required minimum speed which will enable the person cross over.  while As the magnitude of the length tends towards the same magnitude of the height the speed required to cross the moat increases towards infinity and this speed cannot be attained by the person hence he will land in the moat.

Hence we can conclude that The person lands in the moat if the rope's length is very short because The speed of the platform is less than the required minimum speed  and  The person lands in the moat if the rope length is similar to the height of the platform because,the speed required to cross the moat approaches infinity.

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When you place leftover food in the refrigerator, what kind of energy do you
decrease in the food?
A. Nuclear energy
B. Electromagnetic energy
C. Thermal energy
D. Chemical energy

Answers

By cooling down the food, the thermal energy in the food molecules is reduced.

What is a refridgerator?

A refrigerator is an appliance that is commonly used in the home for the purpose of cooling down a substnace especially water and drinks.

Due to the fact that the molecules that compose matter are is in a state of constant random motion, the food molecules contain thermal energy. Hence, by cooling down the food, the thermal energy in the food molecules is reduced.

Learn more about thermal energy: https://brainly.com/question/11278589

The plate is a model for how sunlight hits Earth’s surface. Which parts of Earth are most similar to the plate with an axis angle of 0°?

Answers

Answer: The parts closer to the equator.

Explanation:

The parts of the earth closer to the equator are similar to the plate, because they receive more sunlights than other parts. Which makes them hotter than any other regions in the earth. Example of such countries are Gabon, Uganda, Kenya, Maldives, the democratic republic of Congo, sao tome and principle  e.t.c

"What will the pressure inside the container become if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant?"

Answers

This question is incomplete, the complete question is;

The Figure shows a container that is sealed at the top by a moveable piston, Inside the container is an ideal gas at 1.00 atm. 20.0°C and 1.00 L.

"What will the pressure inside the container become if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant?"

Answer:

the pressure inside the container become 0.625 atm if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant

Explanation:

Given that;

P₁ = 1.00 atm

P₂ = ?

V₁ = 1 L

V₂ = 1.60 L

the temperature of the gas is kept constant

we know that;

P₁V₁ = P₂V₂

so we substitute

1 × 1 = P₂ × 1.60

P₂ = 1 / 1.60

P₂ = 0.625 atm

Therefore the pressure inside the container become 0.625 atm if the piston is moved to the 1.60 L mark while the temperature of the gas is kept constant

What amount of work is done on a cart that is pushed 4.0 meters across a floor by a horizontal 40-N net force?

Answers

Answer:

The answer is 160 J

Explanation:

The work done by an object can be found by using the formula

workdone = force × distance

From the question we have

workdone = 40 × 4

We have the final answer as

160 J

Hope this helps you

2. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this week. She must get from one side of the school to the other by hurrying down three different hallways. She runs down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she 4covers its 48.0 m length at a speed of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0 m length at a speed of 5.00 m/s. How long does it take Suzette to make to class? Did Suzette beat the bell?

Answers

Answer:

62 secondsno

Explanation:

The total travel time Suzette experiences is the sum of the times in each hallway. Using

  time = distance/speed

we can add the times.

  (35.0 m)/(3.50 m/s) +(48.0 m)/(1.20 m/s) +(60 m)/(5.0 m/s)

  = 10 s + 40 s + 12 s

  = 62 s

It takes Suzette 62 seconds to get to class. She does not beat the bell.

Engineers are using computer models to study train collisions to design safer
train cars. They start by modeling an elastic collision between two train cars
traveling toward each other. Car 1 is traveling north at 20 m/s and has a mass
of 12,745 kg. Car 2 is traveling south at 15 m/s and has a mass of 4,125 kg.
After the collision, car 1 has a final velocity of 3 m/s north. What is the final
velocity of car 2?
A. 56 m/s north
B. 56 m/s south
C. 38 m/s south
D. 38 m/s north

Answers

Answer:

did you get the answer???

Answer: 38 m/s north

Explanation:

The light bulbs are identical. Initially both bulbs are glowing. What happens when the switch is closed

Answers

Answer:

They turn off

Explanation:

kerosene is able to reach the oher end of a wick by

Answers

Answer:

Capillary Action

Explanation:

Narrow spacings or pores are present in the wick, due to which capillary action takes place, that makes the oil to reach the other end of wick.  The ability of a liquid to flow in narrow spaces without any opposition or assistance of external force such as gravity is called as Capillary action.
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