Question

Calculate the scalar product of the following vectors.
Find the coordinates of the vector x which is collinear with the vector $a=2i+j-k$ and satisfies the condition $x\cdot a=3.$

Answer 1

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

here b is some scalar

$a.x=b\overrightarrow{a}.\overrightarrow{a}=3$

$b(2,1,-1).(2,1,-1)=3$

$b=\frac{3}{6}$

$b=\frac{1}{2}$

$\overrightarrow{a}=\frac{1}{2}(2,1,-1)=(1,0.5,-0.5)$