g Find the equation of the line passing through the point (1, 1, 1) which is perpendicular to the plane containing the points (1, 0, 0), (2, 1, 1) and (1, 1, 2).

Answers

Answer 1

Answer:

The equation of the line is given by:

[tex]x = 1 + t[/tex]

[tex]y = 1 - 2t[/tex]

[tex]z = 1 + t[/tex]

Step-by-step explanation:

Parametrizing the equation of the line in function of t, the equation of the line is given by:

[tex]x = x_0 + at[/tex]

[tex]y = y_0 + bt[/tex]

[tex]z = z_0 + ct[/tex]

In which we have an initial point [tex](x_0,y_0,z_0)[/tex] and [tex](a,b,c)[/tex] is a vector parallel to the line.

Line passing through the point (1, 1, 1)

This means that [tex]x_0 = y_0 = z_0 = 1[/tex]. So

[tex]x = 1 + at[/tex]

[tex]y = 1 + bt[/tex]

[tex]z = 1 + ct[/tex]

Perpendicular to the plane containing the points (1, 0, 0), (2, 1, 1) and (1, 1, 2).

From this, we get two vectors:

[tex](2-1,1-0,1-0) = (1,1,1)[/tex]

[tex](1-2,1-1,2-1) = (-1,0,1)[/tex]

The parallel vector is given by the determinant of the following matrix:

[tex]\left[\begin{array}{ccc}i&j&k\\1&1&1\\-1&0&1\end{array}\right][/tex]

Which is:

[tex]D = i*1*1 + j*1*-1 + k*1*0 - k*1*(-1) - j*1*1 -i*1*0[/tex]

[tex]D = i - j + k - j[/tex]

[tex]D = i - 2j + k[/tex]

So the vector is (1,-2,1), and the equation of the line is:

[tex]x = 1 + t[/tex]

[tex]y = 1 - 2t[/tex]

[tex]z = 1 + t[/tex]


Related Questions

Say on g this is what you will wish for if you only had 3 wishes
1. Unlimited money
2. Unlimited bx tches
3. More wishes

Answers

Step-by-step explanation:

Unlimited money

ay u know how it is with unlimited money

i buy arab countries with them oils innit

And buy a large shares of big companies like Microsoft ,Apple Tesla , SpaceX .. u name it

Help pls I no it’s simple but I don’t understand pls look at the pictures or image pls pls number 1 pls

Answers

Answer: The answer would be No, Yes, No.

Step-by-step explanation:

Look at the grid, you can see that it has 100 units in all.

0.42 equals 21/50, so they are both wrong. The denominator would have to be 100. The only logical one would be the second one.

One meter of electrical cord costs 3 dollars. How much should one pay for...

2/3 meters?

Answers

2/3 of 3 is 2 because u just get that
$2 because 2/3 is 2 so you would pay $2 for only 2/3 meters

Two numbers are in the ratio of 5:6. Their sum is 77. What is the positive difference between the two numbers?

Answers

Answer:

7

Step-by-step explanation:

a:b = 5:6

∃x such that a=5x and b=6x

a+b = 77

5x+6x = 77

x = 7

a = 5x = 35

b = 6x = 42

42-35 = 7

A boy walked to the store with 3 apples. He dropped two of them. How many does he have left. PLEASE HELP

Answers

Answer:

Doesnt he still have 3? All he did was drop 2

Step-by-step explanation:

A bookshelf is 42 inches long.
How many books of length 1 and 1/2 inches will fit on the bookshelf?

Answers

Answer:

33

Step-by-step explanation:

What is the value of 3 + 1 when n = 4?
13
7
8
12

Answers

Answer:

13

Step-by-step explanation:

3n=12+1=13

Part 2 from my other worksheet!

Help me! I’ll mark you brainly!

Answers

Answer:

i cant even read the word there too small  

Step-by-step explanation:

Use FOIL to expand and simplify:

Triangle Tiger:

A = (2x + 6)(x - 4)

= 2x^2 -8x + 6x - 24

= 2x^2 - 2x - 24 ft^2 (N)

Anthony's Computer Monitor:

A = (x - 3)(2x + 1)

= 2x^2 + x - 6x - 3

= 2x^2 - 5x - 3 in^2 (I)

Art Class:

A = (x - 4)^2

= x^2 - 8x + 16 in^2 (O)

Easel:

A = [(2x - 5)(2x + 4)] / 2

= (4x^2 + 8x - 10x - 20) / 2

= (4x^2 - 2x - 20) / 2

= 2x^2 - x - 10 in^2 (E)

Four Square:

A = (x + 2)^2

= x^2 + 4x + 4 ft^2 (A)

What is the slope of the line graphed below?

Answers

Answer:

d. -3

Step-by-step explanation:

1/4x+2=-4 how do you do this step by step?​

Answers

It’s a process of bringing one variable to the side with different forms of mathematical properties. First, subtract 2 from the left side and add it to the right side. Then divide 1/4x by 1/4 to get x alone, and divide the right side (-2) by 1/4, which will give you the answer to x. Let me know if you need help with anything else!

Answer: Solution

=

2

4

Step-by-step explanation: Combine multiplied terms into a single fraction

1

4

+

2

=

4

1

4

+

2

=

4

Multiply by 1

1

4

+

2

=

4

4

+

2

=

4

Subtract  

2

2

2

from both sides of the equation

Eight oranges cost $1.00. How much will 4 dozen oranges coste
Gm

Answers

Answer:

Step-by-step explanation:

if 8 oranges cost 1 dollars

4 oranges cost 1/2=0.50 cents

one dozen=4*3= 12 oranges

0.50*3=1.50 dollars/dozen

4 dozen=4*1.50=6 dollars

Cost = $6.00

EXPLANATION:

0 = 1 orange

0 0 0 0 0 0 0 0 = 8 oranges = $1.00

1 dozen = 12 (oranges)

4 dozens = 48 (oranges)

0 0 0 0 0 0 0 0 = $1 (1)

0 0 0 0 0 0 0 0 = $1 (2)

0 0 0 0 0 0 0 0 = $1 (3)

0 0 0 0 0 0 0 0 = $1 (4)

0 0 0 0 0 0 0 0 = $1 (5)

0 0 0 0 0 0 0 0 = $1 (6)

I divided the 48 oranges in groups of 8.

One group of 8 oranges equals $1.

There was a total of 6 groups of 8 oranges, without any leftovers.

The Total Is $6.

Graph for f(x)=6^6 and f(x)=14^x

Answers

Graph Transformations

There are many times when you’ll know very well what the graph of a

particular function looks like, and you’ll want to know what the graph of a

very similar function looks like. In this chapter, we’ll discuss some ways to

draw graphs in these circumstances.

Transformations “after” the original function

Suppose you know what the graph of a function f(x) looks like. Suppose

d 2 R is some number that is greater than 0, and you are asked to graph the

function f(x) + d. The graph of the new function is easy to describe: just

take every point in the graph of f(x), and move it up a distance of d. That

is, if (a, b) is a point in the graph of f(x), then (a, b + d) is a point in the

graph of f(x) + d.

As an explanation for what’s written above: If (a, b) is a point in the graph

of f(x), then that means f(a) = b. Hence, f(a) + d = b + d, which is to say

that (a, b + d) is a point in the graph of f(x) + d.

The chart on the next page describes how to use the graph of f(x) to create

the graph of some similar functions. Throughout the chart, d > 0, c > 1, and

(a, b) is a point in the graph of f(x).

Notice that all of the “new functions” in the chart di↵er from f(x) by some

algebraic manipulation that happens after f plays its part as a function. For

example, first you put x into the function, then f(x) is what comes out. The

function has done its job. Only after f has done its job do you add d to get

the new function f(x) + d. 67Because all of the algebraic transformations occur after the function does

its job, all of the changes to points in the second column of the chart occur

in the second coordinate. Thus, all the changes in the graphs occur in the

vertical measurements of the graph.

New How points in graph of f(x) visual e↵ect

function become points of new graph

f(x) + d (a, b) 7! (a, b + d) shift up by d

f(x) Transformations before and after the original function

As long as there is only one type of operation involved “inside the function”

– either multiplication or addition – and only one type of operation involved

“outside of the function” – either multiplication or addition – you can apply

the rules from the two charts on page 68 and 70 to transform the graph of a

function.

Examples.

• Let’s look at the function • The graph of 2g(3x) is obtained from the graph of g(x) by shrinking

the horizontal coordinate by 1

3, and stretching the vertical coordinate by 2.

(You’d get the same answer here if you reversed the order of the transfor-

mations and stretched vertically by 2 before shrinking horizontally by 1

3. The

order isn’t important.)

74

7:—

(x) 4,

7c’

‘I

II

‘I’

-I

HELPPPPPPPP DUE TODAYYYY!!!!!!!!!!!!! WORTH 30 POINTS!!!!!!!!!

Answers

Answer:

4.5

Step-by-step explanation:

Peppa's brother George spilled milk on her math
homework and all she can see are two points in her
table. The points are (3, 8) and (10, 2335.43). Peppa
still has to find the equation representing the values in
her table.
Explain to Peppa how to find the equation (y= a(b))
using her two points and write the exponential equation.
Explain and show work for every step.

Answers

Answer:

i need help with this one

Step-by-step explanation:

Jenny is shopping at Fashion Island in Newport Beach for a new winter jacket and finds one on sale for 25% off the original price. The jacket's original price is $249.99. What is the dollar amount Jenny will save with the 25% discount?

Answers

Answer:

She will save $62.50 and the new amount is 187.49 jut in case

Step-by-step explanation:

Graph the function.
f(x) = square root x+1

Answers

put the equation in desmos graphing calculator. it will show you the graph and you can copy it easily!

hope this helps!
This is what I got!!!!!!!!

Consider the game of rock-paper-scissors to be a random experiment. How many outcomes are in the sample space of this random experiment

Answers

Answer: There are 9 outcomes in this experiment.

Step-by-step explanation:

Rock-Paper- Scissor is a simple game, in which Rock beats scissor, scissor beats paper, paper beats rock. If any two people made the same gesture it will be a tie.

So if two roommates are playing the game , total outcomes in the sample space = 3 x 3   [By fundamental principal of counting]

= 9

Hence, there are 9 outcomes in this experiment.

what is the value of x

Answers

Answer:

124°.

Step-by-step explanation:

x+24°+32°=180° (sum of angles is 180°)

⟹x+56°=180°⟹ x=180°–56°=124°.

find each unit price which is the better buy explain electrical wire $1.89 for 3 ft 89 for 18 in

Answers

Answer:

It all comes down to simplifying it to inches and price so id 18 in” is 0.89 cent’s thats every inch of that 18 is about 4 cents a in” and a $1.89 3 feet is about 5 cent’s

Step-by-step explanation:

So is the first would be a better deal because it is one cent cheaper!

8^3-9×2÷3 I Need Help

Answers

Answer:

506

Step-by-step explanation:

Following PEMDAS you'd start with your exponent

8^3-9×2÷3

Then you'd move on to multiplication

512-9×2÷3

Then do the division

512-18÷3

Then finish the problem by subtracting these two

512-6

Answer:

506

Step-by-step explanation:

just follow PEMDAS

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

The sum of 3 times d and e

Answers

Answer:

there isnt a picture

Step-by-step explanation:

Need help this is urgent!!!

Answers

Answer:

5 units

Step-by-step explanation:

bc = ad

0.57319 kg to cg need this asap

Answers

Answer:

57319 Centigrams

Step-by-step explanation:

You would just multiple 0.57319 by 100,000.

Hope this helps! :)

Answer:

1 kilogram=100,000 centigram

0.57319 kilogram=0.57319 ×100,000= 57319 centigram

57319 centigram is the right answer.

g(x)=3-x
what is
g(h^2) =
g(x+2)=
g(x)+g(2)=

Answers

G(h^2) = 3-h^2
G(x+2)= -x+1
G(x)+g(2)= -X + 4

The length of a rectangle is four more than its width. If the area of the rectangle is 12, find the length of the rectangle.

Answers

Answer:

I don’t know but I have the same question with different numbers

Step-by-step explanation:

Libby earns a mean of 92.9 points with a standard deviation of 5.5 points in her math classes and a mean of 90.3 with a standard deviation of 6.1 points in her history classes. Both distributions are skewed left. If a sample of 30 of her math scores and 31 of her history scores is randomly selected, what is the probability that her mean math score will be more than her mean history score?

0.0401
0.0686
0.9314
0.9599

Answers

Answer:

D. 0.9599

Step-by-step explanation:

I need helps pls :)

Answers

In regular polygons, if the number of sides, n, is odd, the lines of symmetry will pass through a vertex and the half of the opposite side.
Step-by-step explanation:
This is equivalent to say that a perpendicular bisector of a side of the regular polygon bisects the angle of the opposite vertex to the side, and divide the polygon into two symmetrical parts.

For questions 9 and 11, solve for the remaining angles.

Answers

Answer:

Side a = 442.85

Side b = 270

Side c = 255

Angle ∠A = 114.998° = 114°59'54" = 2.0071 rad

Angle ∠B = 33.544° = 33°32'37" = 0.58545 rad

Angle ∠C = 31.458° = 31°27'29" = 0.54905 rad

Step-by-step explanation:

Side a = 442.85

Side b = 270

Side c = 255

Angle ∠A = 114.998° = 114°59'54" = 2.0071 rad

Angle ∠B = 33.544° = 33°32'37" = 0.58545 rad

Angle ∠C = 31.458° = 31°27'29" = 0.54905 rad

F(x) x2+1
What is f(f(x))

Answers

Step-by-step explanation:

(×) x ×2 + 1

x= 2+1

×= 3

3.2 +1 = x

6+1 = 7

×=7

F = (7)

37/16 rounded by the nearest hundredth.

Answers

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Answer:

2.31

Step-by-step explanation:

yup thats the answer

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