Question

Calculate the scalar product of the following vectors.
Find the vector a which is collinear with the vector $b=\{1,-3,1\}$ and satisfies the condition $a\cdot b=22.$

Answer 1

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

here $x$ is some scalar

$a.b=x\overrightarrow{b}.\overrightarrow{b}=22$

$x(1,-3,1).(1,-3,1)=22$

$x=\frac{22}{11}$

$x=2$

$\overrightarrow{a}=2(1,-3,1)=(2,-6,2)$