# What is the angle between <2,-3,-1 > and < -8,3,-5>?

##### 1 Answer
Feb 29, 2016

cos theta=(<2,-3,-1>*<-8,3,-5>)/((sqrt(2^2+(-3^2)+(-1)^2)) (sqrt((-8)^ 2+3^2+(-5)^2))
=(2(-8)+(-3)(3)+(-1)(-5))/((sqrt(14)sqrt(98))
=$- \frac{20}{\sqrt{1372}}$
$\theta = {\cos}^{-} 1 \left(- \frac{20}{\sqrt{1372}}\right) = {122.68}^{\circ}$

#### Explanation:

To find theta take the inverse cosine of the dot product of the given vectors divided by the product of the magnitude of each of the vectors.