Question

Calculate the scalar product of the following vectors.
Find the vector a which is collinear with the vector $b=\{3,6,6\}$ and satisfies the conditions $a.b=27.$

Answer 1

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

here x is some scalar

$a.b=x\overrightarrow{b}.\overrightarrow{b}=27$

$x(3,6,6).(3,6,6)=27$

$x=\frac{27}{81}$

$x=\frac{1}{3}$

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