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3 years ago

Can i please get help with this question? Thanks in advance

Mathematics

2 answers:

Yakvenalex [24]3 years ago

5 0

The answer is the third choice, "6a+8b."

6a → "6 times a number", where a represents the unknown number.

+8b → "plus 8 times a number", where b represents the unknown number as well.

SOVA2 [1]3 years ago

3 0

so it would be 6 times a number so 6a (a is the non-known number) than + 8 and same with a is it is 6a+8b

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Answer with Step-by-step explanation:

a.Let given vector

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By using the formula

Magnitude of a vector= $\sqrt{x^2+y^2+z^2}$

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector= $\hat{a}=\frac{a}{\mid a\mid}$

By using the formula

The unit vector= $\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k$

b.Let vector b=-2i+4j+2k

$\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6$

$\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}$

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by = $6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}$

The vector in the direction of <-2,4,2> with length 6 is given by = $-\sqrt 6(-i+2j+k)$

c. $\theta=\frac{\pi}{3}$

$\mid v\mid=8$

Let v= $v_x i+v_y j$

$v_x=\mid v\mid cos\theta$

$v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=\mid v\mid sin\theta$

$v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form= $4i+4\sqrt 3j$

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