# What is the angle between < 6 , 1 , -4 >  and  < 2 , -3 , 2 > ?

Jan 28, 2016

${88}^{\circ}$

#### Explanation:

To find the angle between 2 vectors use the following formula :

 costheta =( veca.vecb)/((|veca| xx |vecb|)

where a and b represent the 2 vectors and
$\theta \textcolor{b l a c k}{\text{ the angle between them}}$

let $\vec{a} = \left(6 , 1 , - 4\right) , \vec{b} = \left(2 , - 3 , 2\right)$

then $\vec{a} . \vec{b} = 12 - 3 - 8 = 1$

and $| \vec{a} | = \sqrt{{6}^{2} + {1}^{2} + {\left(- 4\right)}^{2}} = \sqrt{36 + 1 + 16} = \sqrt{53}$

$| \vec{b} | = \sqrt{{2}^{2} + {\left(- 3\right)}^{2} + {2}^{2}} = \sqrt{4 + 9 + 4} = \sqrt{17}$

hence $\cos \theta = \frac{1}{\sqrt{53} \times \sqrt{17}}$

$\theta = {\cos}^{-} 1 \left(\frac{1}{\sqrt{901}}\right) = {88}^{\circ}$