Since vector a = 3i - 2j - k and vector b = i + 4j + k, the unit vector, n, normal to the plane is (7i - j + 7k)/3√11 where a, b and n, in this order, form a right-handed system.
The normal vector to the planeThe normal vector to the plane is c = a × b
Since a = 3i - 2j - k and b = i + 4j + k,
c = a × b
c = (3i - 2j - k) × (i + 4j + k)
= 3i × i + (- 2j) × i + (-k) × i + 3i × 4j + (- 2j) × 4j + (-k) × 4j + 3i × k + (- 2j) × k + (-k) × k
= 3i × i - 2j × i - k × i + 12i × j - 8j × j - 4k × 4j + 3i × k - 2j × k - k × k
Given that
i × j = k, k × i = j, j × k = i, j × i = -k, i × k = -jk × j = -i, i × i = 0, j × j = 0 and k × k = 0. we havec = 3(0) - 2(-k) - (-j) + 12k - 8(0) - 16(-i) + 3(-j) - 2i - 0
c = 0 + 2k + j + 12k - 0 + 16i - 3j - 2i
c = 16i - 2i + j - 3j + 2k + 12k
c = 14i -2j + 14k
Unit vector normal to the plane nThe unit vector normal to the plane n = c/|c| where |c| is the magnitude of c = √(14² + (-2)² + 14²) = √(196 + 4 + 196)
= √396
= √(36 × 11)
= 6√11
So, n = c/|c|
= (14i -2j + 14k)/6√11
= 2(7i - j + 7k)/6√11
= (7i - j + 7k)/3√11
So, the unit vector normal to the plane is (7i - j + 7k)/3√11
Learn more about unit vector normal to a plane here:
https://brainly.com/question/14927658
$3.49/ gallon and other is $1.25/L which container of milk is a better deal
Valid Expressions are; t = ∛(d²/va), a = d/t², a = √(vd/t³), v = at
while the Invalid expressions are; v = a/t and d = at
Explanation:
Given expressions
1) v = a/t
2) t = ∛(d²/va)
3) d = at
4) a = d/t²
5) a = √(vd/t³)
6) v = at
First we get our units of parameters
V = m/s, t = sec, d = m, a = m/s²
so
1)
v = a/t
we substitute in our units of parameters
v = m/s² / s = m/s² × 1/s = m/s³
v ≠ m/s³
therefore it is false
2)
t = ∛(d²/va)
we substitute
t = ∛(m² / m/s × m/s²)
t = ∛(m² / m²/s³)
t = ∛(s³)
t = s
correct, the expression is true
3)
d = at
we substitute
d = m/s² × s
d = m/s² × s/1 = ms/s² = m/s
d ≠ m/s (because d = m)
so expression is false
4)
a = d/t²
we substitute
a = m / s² = m/s²
correct
the expression is true
5)
a = √(vd/t³)
we substitute
a = √(m/s×m / s³) = √(m²/s / s³) = √(m²/s × 1/s³) = √(m²/s⁴) = m/s²
so a = m/s²
correct
the expression is true
6)
v = at
we substitute in the units
v = m/s² × s = m/s² ×s/1 = ms/s² = m/s
v = m/s
correct
the expression is correct
How would the conduction of someone’s hand holding the cold water jar affect the jar’s temperature?
Answer:
The person's hand will warm up the jar
Explanation:
Thermal energy will be conducted from his hand to the jar
A body travels at an initial speed of 2.5 m/s. Given a constant acceleration of 0.2 m/s 2 what is the speed of the body at time 25 seconds later?
Answer:
We are given:
u = 2.5 m/s
a = 0.2 m/s/s
t = 25 seconds
v = v m/s
Solving for 'v':
From the first equation of motion:
v = u + at
Replacing the values
v = 2.5 + (0.2)(25)
v = 2.5 + 5
v = 7.5 m/s
How does
friction affect the motion of
two objects sliding past
each other
Friction affects the motion of two objects sliding past each other. This frictional force results into the loss of energy and hence slow down the motion of the two objects in contact.
What is the Frictional force?Frictional force is the force that is resisting the relative motion of solid surfaces, fluid layers, and the two material elements which are sliding against each other. There are several types of friction such as dry friction, it is a force that opposes the relative lateral motion of the two solid surfaces which are in contact.
Frictional force generates when the two surfaces slide past one another in motion. The force of friction opposes the motion of an object which is in contact, causing the moving objects to lose energy and slow down. The frictional force is important as it helps us in walking, driving a car, and in doing other works.
Learn more about Friction here:
https://brainly.com/question/13000653
#SPJ6
ANSWER PLS
Heat moves from the land to the air through the process of
conduction
convection
radiation
refraction
Answer:
Conduction
Explanation:
conduction is one of the three main ways that heat energy moves from place to place the other two ways heat moves around our radiation and convection conduction is the process by which heat energy is transmitted through Collisons between neighboring atoms or molecules.
hope this helps :)
Answer:
A
Explanation:
During a care on level ground, Andra runs with an average velocity of 6.02 m/s to the East. What distance does Andra cover in 137 seconds?
Answer:
The distance covered is: 824.74 meters
Explanation:
Use the formula for velocity (v) as the distance (d) covered over the time (t) it took:
v = d / t
in our case:
6.02 m/s = d / 137 s
d = 6.02 * 137 = 824.74 meters
What is it called when two waves meet?
Question 1 options:
frequency
resonance
amplitude
superposition
Superposition is the most correct option
When two waves meet it is generally called inteference. Superposition occurs when the waves adds up to form a stronger wave. This is called constructive interference
hope this helps....
Name the charcteristic which help us distinguish berween aman's voice and awamen's seeing them
Answer:
Asalamalikum maryam
Following are the characteristics that help to distinguish between man's and women's voice
Mans have low pitched sound while as women have hight pitched sound.Mans voice is thick while as women's voice is thin.find the kenitic energy before and after the collision
Answer:
The total system kinetic energy before the collision equals the total system kinetic energy after the collision. If total kinetic energy is not conserved, then the collision is referred to as an inelastic collision.
Explanation:
Initial kinetic energy KE = 1/2 m1v12 + 1/2 m2v22 = joules. The following calculation expects you to enter a final velocity for mass m1 and then it calculates the final velocity of the other mass required to conserve momentum and calculates the kinetic energy either gained or lost to make possible such a collision.
A) The motor speed is less than wheel speed.
B) The output power of the motor is positive during hill climbing.
C) The wheel torque is more than motor torque.
For the following statements
A) The motor speed is less than wheel speed.
B) The output power of the motor is positive during hill climbing.
C) The wheel torque is more than motor torque
These assertions are given respectively as
falsetruefalseWhat are speed, power, and Torque?Speed: defined as the ratio of operation with respect to distance and time
Power: defined as the ability to work
Torque: This is the speed of a rotating object
Generally, the equation for Speed, Power, Torque is mathematically given as
V=m/s
P=w/t
T=rfsin\theta
In conclusion
For a moving car, the wheels speed is in equilibrium with the motor speed Hence false
The output power during a hill climb is positive cause work is been done, Hence true
The wheel torque also is in equilibrium with the motor Torque, Hence false
Read more about Work
https://brainly.com/question/756198
. Satisfied with the jeweler’s method, the customer next takes out a large and rigid bracelet, adds it to the measuring container and records the new mass and the volume level of the liquid, planning to use the same method to determine what it is made of. Unfortunately, the customer failed to notice that the bracelet was much larger than the ring, and was not fully submerged, but was partially protruding above the surface of the water. Do you believe that the density the customer calculated was higher or lower than the actual density of the bracelet? Explain how you came to your conclusion.
Answer:
value is obtained than the real one.
ρ > ρ_real
Explanation:
A widely used method to determine the density of a body is to measure its mass and measure its volume by immersing it in a transparent liquid, to measure its volume by the difference in volumes of the liquid then use the relationship
ρ = m / V
In this case, part of the body remains the force of the liquid, in this case using Archimedes' principle that establishes that the weight of the desalted liquid is equal to the thrust, let's use the equilibrium equation
B - W = 0
B = W
ρ_liquid g V_submerged = ρ_body g V_body
V_submerged = (ρ_body /ρ-liquid) V_body
We can see that the volume is only a fraction of the volume of the body, therefore when performing the division a higher value is obtained than the real one.
Megan walks 100 m east and then travels 70 m north followed by 140 m
east. What is the total distance she travels? Show/explain how you
calculate. *
Answer:
I think it's just 100+70+140
What causes the shock you receive from when you touch a doorknob?
Neutrons being pulled from one
surface to another
Protons being pulled from one surface to another
Electrons being pulled from one surface to another
Positrons being pulled from one surface to another
Answer:
Electrons being pulled from one surface to another
Explanation:
The movement of electrons creates electrical charge.
A pulley of radius 8.0 cm is connected to a motor that rotates at a rate 7000 rad s-1 and then decelerate uniformly at a rate of 2000 rad s-1 within 5 s.
a. Calculate its angular acceleration.
b. What is the number of rotations within the time range?
c. How long is the string that winds it within the time range?
d. Determine the tangential acceleration of the string.
[15 marks]
Answer:
(a) α = - 1000 rad/s²
Negative sign represents deceleration.
(b) θ = 3581 rotations
(c) L = 1800 m
(d) a = - 80 m/s²
Explanation:
(a)
using First equation of motion for angular motion:
ωf = ωi + αt
where,
ωf = Final Angular Speed = 2000 rad/s
ωi = Initial Angular Speed = 7000 rad/s
α = Angular Acceleration = ?
t = time = 5 s
Therefore,
2000 rad/s = 7000 rad/s + α(5s)
α = (2000 rad/s - 7000 rad/s)/5 s
α = - 1000 rad/s²
Negative sign represents deceleration.
(b)
Using second equation of motion:
θ = ωi t + (1/2)αt²
where,
θ = No. of Rotations = ?
Therefore,
θ = (7000 rad/s)(5 s) + (1/2)(- 1000 rad/s²)(5 s)²
θ = 35000 rad - 12500 rad
θ = (22500 rad)(1 rotation/2π rad)
θ = 3581 rotations
(c)
Length of String = L = (Circumference of Pulley)(θ)
L = [2π(0.08 m)][3581 rotations]
L = 1800 m
(d)
Tangential Acceleration = a = rα
a = (0.08 m)(-1000 rad/s²)
a = - 80 m/s²
Which of these factors determine the brightness of a star?*
O The size of the star
The surface temperature of the star
The distance the star is from the Earth
O All of the above
Answer:
All of Above
Explanation:
Dominic made the table below to organize his notes about mixtures. A 1-column table. The first column labeled properties of mixtures has entries has no set composition, must have more than one state of matter, must have more than one substance. What mistake did Dominic make? The title should read “Properties of Solutions” because some mixtures do not have all of the properties listed. There is a definite recipe to make each mixture, so the composition of a mixture is set. Although it is possible to have more than one state, it is also possible to have only one state. A single substance can be used to make a mixture if the substance is composed of more than one element.
Answer:
The is: Although it is possible to have more than one state, it is also possible to have only one state.
Explanation:
Hope this helps! ;-)
Answer:
Although it is possible to have more than one state, it is also possible to have only one state.
Explanation:
10. The force with which one thing hits another or with which two objects collide is
a. Impact force
b. Motion force
c. External force
d. Internal force
Impact force
What is impact force?Impact force is the force exerted by bodies when they come in contact. Impact force has same unit as force. it is similar to impulse the difference is that impulse considers time.
hope it helps...
What are the two types of techniques used when playing tennis? Please provide your answer using a complete sentence.
The serve, forehand groundstroke, backhand groundstroke, forehand volley, backhand volley, and overhead smash are the six basic strokes in tennis. The 6 basic "strokes" are the basic actions a tennis player makes to hit the ball.
Stay safe & humble <3
a starting A resultant force of 25 Newton's act on a mass of 0.50kg starting from rest find acceleration in m/s2,final velocity after 20 minutes, distance moved in 20 minutes
Answer:
Using Newton's second law of motion;
F=ma
25=0.25a
a=25/0.25=100 m/s²
After 20 minutes;
Vf=at+Vi
Vf=100(1200)+0
Vf=120000 m/s
d=at²/2 +Vi×t
d=100(1200)²+0
d=144 000 000 meters
A series circuit contains both a 6Ω and a 3Ω resistor. Through the 6Ω resistor, the current is 0.5 amps. What will the current be through the 3Ω resistor?
Answer:
0.5 amps
Explanation:
the amps will be constant no matter what
Consider the interference pattern produced by two parallel slits of width a and separation d, in which d = 3a. The slits are illuminated by normally incident light of wavelength λ.
Required:
a. First we ignore diffraction effects due to the slit width. At what angles θ from the central maximum will the next four maxima in the two-slit interference pattern occur?
b. If the intensity at θ = 0 is I0, what is the intensity at each of the angles in part (a)?
c. Which double-slit interference maxima are missing in the pattern?
Answer:
a) m =1 θ = sin⁻¹ λ / d, m = 2 θ = sin⁻¹ ( λ / 2d) , c) m = 3
Explanation:
a) In the interference phenomenon the maxima are given by the expression
d sin θ = m λ
the maximum for m = 1 is at the angle
θ = sin⁻¹ λ / d
the second maximum m = 2
θ = sin⁻¹ ( λ / 2d)
the third maximum m = 3
θ = sin⁻¹ ( λ / 3d)
the fourth maximum m = 4
θ = sin⁻¹ ( λ / 4d)
b) If we take into account the effect of diffraction, the intensity of the maximums is modulated by the envelope of the diffraction of each slit.
I = I₀ cos² (Ф) (sin x / x)²
Ф = π d sin θ /λ
x = pi a sin θ /λ
where a is the width of the slits
with the values of part a are introduced in the expression and we can calculate intensity of each maximum
c) The interference phenomenon gives us maximums of equal intensity and is modulated by the diffraction phenomenon that presents a minimum, when the interference reaches this minimum and is no longer present
maximum interference d sin θ = m λ
first diffraction minimum a sin θ = λ
we divide the two expressions
d / a = m
In our case
3a / a = m
m = 3
order three is no longer visible
(a) The next four angles from the central maxima are sin⁻¹ λ / d, sin⁻¹ λ / 2d , sin⁻¹ λ / 3d, and sin⁻¹ λ / 4d respectively.
(b) With the values of part a are the expression of intensity of each maximum can be calculated accordingly.
(c) The third order maxima (m = 3) is missing from the pattern obtained through the double-slit experiment.
a)
In the interference phenomenon the maxima are given by the expression
d sin θ = m λ
Here,
d is the slit separation and m is the order of interference.
The maximum for m = 1 is at the angle is,
θ = sin⁻¹ λ / d
For the second maximum m = 2
θ = sin⁻¹ ( λ / 2d)
For the third maximum m = 3
θ = sin⁻¹ ( λ / 3d)
For the fourth maximum m = 4
θ = sin⁻¹ ( λ / 4d)
Thus, we can conclude that the next four angles from the central maxima are sin⁻¹ λ / d, sin⁻¹ λ / 2d , sin⁻¹ λ / 3d, and sin⁻¹ λ / 4d respectively.
b)
Considering the effect of diffraction, the intensity of the maximums is modulated by the envelope of the diffraction of each slit.
I = I₀ cos² (Ф) (sin x / x)²
Where Ф is the phase angle, and its value is,
Ф = π d sin θ /λ
x = π a sin θ /λ
Here a is the width of the slits
Thus, with the values of part a are introduced in the expression the intensity of each maximum can be calculated accordingly.
c)
The interference phenomenon gives us maximums of equal intensity and is modulated by the diffraction phenomenon that presents a minimum, when the interference reaches this minimum and is no longer present.
For the maximum interference:
d sin θ = m λ
For the first diffraction minimum:
a sin θ = λ
Dividing both the expressions as,
d / a = m
Since, d = 3a. Then,
3a / a = m
m = 3
Thus, we can conclude that the third order maxima (m = 3) is missing from the pattern obtained through the double-slit experiment.
Learn more about the interference here:
https://brainly.com/question/16098226
Forces in action worksheet. Need help with this, it's due tomorrow by 8:30am, please help! If you do the bottom 2 for me as well, I will mark brainliest :)
What is occurring when two waves traveling along the same medium meet and cancel each other out?
O destructive interference
O constructive interference
O reflection
O refraction
Answer:
Destructive interference
Explanation:
Destructive interference occurs when two waves traveling along the same medium meet and cancel each other out. The resultant wave has a smaller amplitude than the individual waves. In this case, the maxima of two waves are 180 degrees out of phase.
Hence, the correct option is (A) "destructive interference"
Answer: the answer is A. Destructive inference
Explanation: I took the test
3. What kinds of electromagnetic waves have the lowest frequencies? What kinds have the highest frequencies?
Answer:
Explanation:
from highest to lowest frequency
gamma-ray, x-ray, ultraviolet, visible light, infrared, microwave, radio
hope this helps have a good day :)
The electromagnetic waves with the lowest frequencies are the ones we call "radio" waves.
The electromagnetic waves with the highest frequencies are the ones we call "gamma rays".
In between those are all the others . . . the microwaves, the heat ('thermal') waves, the infrared waves, the light waves, the ultraviolet waves, and the X-rays.
Which item has the most thermal energy?
Answer:
room temperature water
Explanation:
Answer:
In the figure, the particles of cocoa are moving faster than the particles of bathwater. Therefore, the cocoa has a higher temperature. However, the bath water has more thermal energy because there is so much more of it. It has many more moving particles.
Explanation:
A grinding wheel with a moment of inertia of 2.0 kg•mº is initially at rest. What angular momentum will the wheel have 10.0 s after a 2.5 N·m torque is applied to it?
a. 25 kg•m/s
b. 4.0 kg•m/s
c. 7.5 kg•m/s
d. 0.25 kg•m/s
Answer:
25 kg m^2/s
Explanation:
The angular acceleration due to the application of torque to the grinding wheel is:
[tex]\tau=I\alpha \rightarrow \alpha=\frac{2.5}{2}=1.25[/tex] (in radian per square second)
So, by the basic equation of the angular acceleration, we can get the angular velocity at t = 10 s as follows:
[tex]\omega=\omega_{o}+\alpha t \rightarrow \omega =0+(1.25)(10) =12.5[/tex] rad/s.
So, the angular momentum at t = 10 s:
[tex]L=I\omega=(2)(12.5) = 25[/tex] kg m^2/s
At t = 0, Ball 1 is dropped from the top of a 22 m-high building. At the same instant Ball 2 is thrown straight up from the base of the building with an initial velocity of +12 m/s. Assume that Ball 1 starts from rest and that air friction can be ignored. At what height will the two balls pass each other? What is the velocity of each ball at the moment they are at the same height?
Answer:
The two balls pass each other at a height of 5.53 m
vf1=17.97 m/s
vf2=-5.96 m/s
Explanation:
Vertical Motion
An object thrown from the ground at speed vo, is at a height y given by:
[tex]y=vo.t-g.t^2/2[/tex]
Where t is the time and [tex]g=9.8\ m/s^2[/tex]
Furthermore, an object dropped from a certain height h will fall a distance y, given by:
[tex]y=g.t^2/2[/tex]
Thus, the height of this object above the ground is:
[tex]H = h-g.t^2/2[/tex]
The question describes that ball 1 is dropped from a height of h=22 m. At the same time, ball 2 is thrown straight up with vo=12 m/s.
We want to find at what height both balls coincide. We'll do it by finding the time when it happens. We have written the equations for the height of both balls, we only have to equate them:
[tex]vo.t-g.t^2/2=h-g.t^2/2[/tex]
Simplifying:
[tex]vo.t=h[/tex]
Solving for t:
[tex]t=h/vo=22/12=1.833\ s[/tex]
The height of ball 1 is:
[tex]H = 22-9.8.(1.833)^2/2[/tex]
H = 5.53 m
The height of ball 2 is:
[tex]y=12\cdot(1.833)-9.8\cdot(1.833)^2/2[/tex]
y=5.53 m
As required, both heights are the same.
The speed of the first ball is:
[tex]vf1=g.t=9.8\cdot 1.833=17.97\ m/s[/tex]
vf1=17.97 m/s
The speed of the second ball is:
[tex]vf2=vo-gt=12-9.8\cdot 1.833=-5.96\ m/s[/tex]
vf2=-5.96 m/s
This means the second ball is returning to the ground when both balls meet
A 2-kg ball is moving with constant speed of 5 m/s in a horizontal circle whose radius is 50 cm. What is the magnitude of the net force on the ball
For a 2-kg ball moving with a constant speed of 5 m/s in a horizontal circle whose radius, the magnitude of the net force on the ball is 50 cm. is mathematically given as
F= 100 N
What is the magnitude of the net force on the ball?Generally, the equation for the Net force is mathematically given as
F = m*r*w^2
Where
w = angular velocity
w= 5/r
w= 10 rad/s
Therefore
F = 2/0.5/10^2
F= 100 N
Read more about Force
https://brainly.com/question/13370981
What is the volume of a 100g object with a density of 50g/cm3?
A. 5,000cm3
B. 2cm3
C. 0.5cm3
D. 2g
Answer:
The answer is 2 cm³Explanation:
The volume of a substance when given the density and mass can be found by using the formula
[tex]volume = \frac{mass}{density} \\ [/tex]
From the question we have
[tex]volume = \frac{100}{50} \\ [/tex]
We have the final answer as
2 cm³Hope this helps you
Why does the ocean have waves?
Answer:
Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. ... The gravitational pull of the sun and moon on the earth also causes waves.