# If A = <2 ,-5 ,-4 >, B = <-9 ,1 ,9 > and C=A-B, what is the angle between A and C?

Mar 17, 2016

$\frac{\pi}{2}$

#### Explanation:

Angle between two vectors U and V is given by the formula

$\cos \theta$ = $\frac{U . V}{| U | . | V |}$
In the present case
U = A = <2,-5,-4> and V = C = A - B = <-11, 6, 13>
U . V= (2, -5,-4).(-11,6,-13) = -22 -30+52=0

|U|= $\sqrt{{2}^{2} + {\left(- 5\right)}^{2} + {\left(- 4\right)}^{2}}$ = $\sqrt{45}$

|V|= $\sqrt{{11}^{2} + {6}^{2} + {13}^{2}} = \sqrt{326}$

Hence $\cos \theta$ = $\frac{0}{\sqrt{45} . \sqrt{326}}$=0

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