Question

Find the angle between the vectors:

$a=\{-1,2,-2\}$ and $b=\{6,3,-6\}.$

Answer 1

Angle between the vectors

$\overrightarrow{a}=\{-1,2,-2\}$ and

$\overrightarrow{b}=\{6,3,-6\}$

So angle between the vectors is given by

$\cos \theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{a}||\overrightarrow{b}|}$

$\cos \theta =\frac{-1\left(6\right)+2\left(3\right)+12}{\sqrt{4+4+1}\sqrt{36+9+36}}$

$\cos \theta =\frac{12}{3\times 9}$

$\Rightarrow \theta ={\cos }^{-1}\frac{4}{9}$.