# What is the angle between <0,5,4>  and <5,-8,7>?

Dec 21, 2015

$80 , {82}^{\circ}$

#### Explanation:

The inner product of 2 vectors A and B in ${\mathbb{R}}^{3}$ may be given by $A \cdot B = | | A | | | | B | | \cos \theta$ where $\theta$ is the angle between A and B.

$\therefore \left(0 , 5 , 4\right) \cdot \left(5 , - 8 , 7\right) = | | \left(0 , 5 , 4\right) | | \cdot | | \left(5 , - 8 , 7\right) | | \cos \theta$

$\therefore \theta = {\cos}^{- 1} \left(\frac{0 - 40 + 28}{\sqrt{{0}^{2} + {5}^{2} + {4}^{2}} \cdot \sqrt{{5}^{2} + {8}^{2} + {7}^{2}}}\right)$

$= 80 , {82}^{\circ}$