If A = <2 ,4 ,-7 >, B = <3 ,8 ,2 > and C=A-B, what is the angle between A and C?

May 13, 2016

56.78 degrees

Explanation:

C = A-B = < (2-3), (4-8), (-7-2)> = <-1,-4,-9>

||A||= sqrt (2^2 +4^2+(-7)^2= $\sqrt{69}$

||C||= $\sqrt{{\left(- 1\right)}^{2} + {\left(- 4\right)}^{2} + {\left(- 9\right)}^{2}}$ =$\sqrt{98}$

A.C= 2(-1) +4(-4) + (-7)(-9)= 45

If $\theta$ is the angle between A and C,

$\cos \theta = \frac{45}{\sqrt{69} \sqrt{98}}$=0.5479

$\theta$=56.78 degrees