Find the area of the rectangle. a. 44 ft2 b. 64 ft2 c. 196 ft2

Find a decomposition of a=⟨−5,−1,1⟩ into a vector c parallel to b=⟨−6,0,6⟩ and a vector d perpendicular to b such that c+d=a.

dezoksy [38]

The projection of vector A parallel to vector B is $\langle -3, 0, 3\rangle$ and the projection of vector A perpendicular to vector B is $\langle -2, -1, -2\rangle$ .

In this question, we need to determine all projections of a vector with respect to another vector. In this case, the projection of vector A parallel to vector B is defined by this formula:

$\vec a_{\parallel , \vec b} = \frac{\vec a \,\bullet\,\vec b}{\|\vec b\|^{2}}\cdot \vec b$ (1)

Where $\|\vec b\|$ is the norm of vector B.

And the projection of vector A perpendicular to vector B is:

$\vec a_{\perp, \vec b} = \vec a - \vec a_{\parallel, \vec b}$ (2)

If we know that $a = \langle -5, -1, 1 \rangle$ and $\vec b = \langle -6, 0, 6 \rangle$ , then the projections are now calculated:

$\vec a_{\parallel, \vec b} = \frac{(-5)\cdot (-6)+(-1)\cdot (0)+(1)\cdot (6)}{(-6)^{2}+0^{2}+6^{2}} \cdot \langle -6, 0, 6 \rangle$

$\vec a_{\parallel, \vec b} = \frac{1}{2}\cdot \langle -6, 0, 6 \rangle$

$\vec a_{\parallel, \vec b} = \langle -3, 0, 3\rangle$

$\vec a_{\perp, \vec b} = \langle -5, -1, 1 \rangle - \langle -3, 0, 3 \rangle$

$\vec a_{\perp, \vec b} = \langle -2, -1, -2\rangle$

The projection of vector A parallel to vector B is $\langle -3, 0, 3\rangle$ and the projection of vector A perpendicular to vector B is $\langle -2, -1, -2\rangle$ .

We kindly invite to check this question on projection of vectors: brainly.com/question/24160729

7 0

3 years ago

(Geometry) Question 2

Kruka [31]

Answer:

E = {0, 1, 2, 3)

Step-by-step explanation:

Integer: a number with no decimal or fractional part, from the set of negative and positive numbers, including zero
< means less than
> means more than

E = {0, 1, 2, 3)

6 0

2 years ago

15 POINTS! HELP ASAP must be one of the answers

alina1380 [7]

Heres your answer also,

Sorry i took long i had trouble figuing this out.

Hope it helps you tho.

A=36 1/4

L=8 3/4

W=A/L

A=W times L

A=145/4

L=35/4

W=145/4/35/4

W=29/4

thats the answer but you must make it mixed again.

answer W=4 1/7

which makes (A) your answer

7 0

3 years ago

What's the pattern for 1,3,5,7,5,3,1,3

natali 33 [55]

+2,+2,+2,-2,-2,-2,+2,+2,+2 etc

8 0

4 years ago

Evaluate the expression 43-3m for m=6

gregori [183]

If m=6, then 3×6= 18.
$43 - 18 = 25$
Your answer is 25.

8 0

4 years ago