# What is the angle between <1 , -2 , 7 >  and  < 7 , -2 , 2 > ?

Nov 10, 2016

The angle is =63.2º

#### Explanation:

The angle between two vectors is given by the dot product.

vecu.vecv=∥vecu∥*∥vecv∥ costheta
$\theta$ is the angle between the two vectors

Here vecu.vecv=〈1,-2,7〉.〈7,-2,2〉=7+4+14=25
The modulus of the vectors are :

∥〈1,-2,7〉∥ = sqrt(1+4+49) = sqrt(54)

∥〈7,-2,2〉∥= sqrt(49+4+4)= sqrt57

costheta=vecu.vecv/(∥vecu∥*∥vecv∥)=25/(sqrt54*sqrt57)=0.45

theta=63.2º