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

Nov 4, 2016

The angle is =47.2º

#### Explanation:

The angle $\theta$ is given by the dot product definition
vecu.vecv=∥vecu∥*∥vecv∥costheta

costheta=(vecu.vecv)/(∥vecu∥*∥vecv∥)

The dot product =〈-4,-1,1〉.〈-6,-1,-4〉=24+1-4=21

The modulus are $\sqrt{16 + 1 + 1} = 3 \sqrt{2}$ and $\sqrt{36 + 1 + 16} = \sqrt{53}$

$\cos \theta = \frac{21}{3 \sqrt{2} \cdot \sqrt{53}} = 0.68$
theta=47.2º