# What is the angle between <-4,0,-2 > and < -2,-1,4 >?

May 3, 2016

$\frac{\pi}{2}$

#### Explanation:

Angle between two vectors is given by the formula
cos theta= (u.v)/(||u|| ||v||

Dot product u.v in this case is (-4)(-2)+(0)(-1) +(-2)(4)=0.

$| | u | | = \sqrt{16 + 4} = \sqrt{20}$ and ||v||= $\sqrt{4 + 1 + 16} = \sqrt{21}$

Thus $\cos \theta = \frac{0}{\sqrt{420}} = 0$

Hence $\theta = \frac{\pi}{2}$