The graph of y= -2x + 10 is:

compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.

Nina [5.8K]

$\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$

We have been given two vectors $\vec{a}$ and $\vec{b}$ , we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of $\vec{b}$ onto $\vec{a}$ means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

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3 0

1 year ago

What is the value of x? Round to the nearest tenth. Please Help

Elodia [21]

Answer:

Step-by-step explanation:

The segment 20.2 cm is the tangent. Therefore x and 20.2cm are perpendicular.

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

We have

$leg=x,\ leg=20.2cm,\ hypotenuse=(14.7+x)cm$

Substitute:

$x^2+20.2^2=(14.7+x)^2$ <em>use (a + b)² = a² + 2ab + b²</em>

$x^2+408.04=14.7^2+(2)(14.7)(x)+x^2$ <em>subtract x² from both sides</em>

$408.04=216.09+29.4x$ <em>subtract 216.09 from both sides</em>

$191.95=29.4x$ <em>divide both sides by 29.4</em>

$x\approx6.5\ cm$

7 0

3 years ago

a family is building a rectangular fountain in the backyard. the yard is rectangular and measures 8x by 9x. The fountain is goin

densk [106]

Teachers often all this problem a donut problem because it’s like the donut hole getting cut out of the middle. The way that you solve this is to find the area of the whole yard and subtract the area of the fountain. Since they are rectangles we’re going to use A = LW
Area of yard - Area of fountain
A = (8x)(9x) - (2x)(5x)
A = 72 x^2. - 10 x^2
A 62 x^2

5 0

3 years ago

Read 2 more answers

A pair of grant high school hockey fans counted the number of games won by the school each year

Mrrafil [7]

Answer:

8

Step-by-step explanation:

2015: 9 games won

2014: 1 game won

rate of change = 2015 games won - 2014 games won

rate of change = 9 - 1

rate of change = 8

5 0

3 years ago

Given the exponential equation, 3=18. Which of the equationsbelow will solve for x?

Zinaida [17]

Answer:

if you are evaluating this claim is false

7 0

3 years ago