Question

Calculate the scalar product of the following vectors.
Find the vector $b=\{x,y,z\}$ which is collinear with the vector $a=\{2\sqrt{2},-1,4\}if|b|=10.$

Answer 1

if $\overrightarrow{a}iscollinearwith\overrightarrow{b}then\overrightarrow{b}=x\overrightarrow{a}$

here x is some scalar

$|b|=10$

$|x|\overrightarrow{a}=10$

$|x||\overrightarrow{a}|=10$

$|x|\left(5\right)=10$

$|x|=2$

$x=\pm 2$

$a=(4\sqrt{2},-2,8),(-4\sqrt{2},2,-8)$