# What is the angle between <6, 8 ,2 >  and  < -2, 7 ,-2 > ?

Jun 7, 2016

58.7º

#### Explanation:

I assume we are looking for the acute angle $\theta$. If the question asks for the obtuse angle, just find $\theta$ and your answer will be $\pi - \theta$.

Every time we are looking for the acute angle between two direction vectors, we use the dot product:

$a \cdot b = \left\mid a \right\mid \left\mid b \right\mid \cos \theta$
6(–2) + 8(7) + 2(–2) = sqrt(6^2+8^2+2^2)sqrt((–2)^2+7^2+(–2)^2) cos theta
$\cos \theta = \frac{40}{\sqrt{5928}}$
theta = 58.699º ≈ 58.7º (1dp)