# If A = <2 ,6 ,-8 >, B = <-9 ,4 ,-2 > and C=A-B, what is the angle between A and C?

Jan 13, 2017

${50.67}^{o}$

#### Explanation:

C would be <11,2,-6>

Now if the angle between A and C is $\theta$, then $\cos \theta = \frac{A . C}{| A | | C |}$

=(11*2 + 2*6 + (-8)*(-6))/(sqrt(2^2 +6^2 +(-8)^2) sqrt(11^2 +2^2 +(-6)^2)

$= \frac{22 + 12 + 48}{\sqrt{104} \sqrt{161}}$

$= \frac{82}{\sqrt{16744}}$

$= \frac{82}{129.399}$

$= 0.634$

$\theta = {50.67}^{o}$