Question

Calculate the scalar product of the following vectors.
Find the vector a which is collinear with the vector $b=\{2,-1,0\}ifa.b=10.$

Answer 1

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

here x is some scalar

$a.b=x\overrightarrow{b}.\overrightarrow{b}=10$

$x(2,-1,0).(2,-1,0)=10$

$x=\frac{10}{5}$

$x=2$

$\overrightarrow{a}=2(2,-1,0)=(4,-2,0)$