# If A = <4 ,7 ,2 >, B = <7 ,1 ,-4 > and C=A-B, what is the angle between A and C?

Jul 18, 2016

Given

$A = < 4 , 7.2 > \mathmr{and} B = < 7 , 1 , - 4 >$

$\therefore C = A - B = < - 3 , 6 , 6 >$

If the angle betwee A and C be $\theta$ then

$\cos \theta = \frac{A . C}{\left\mid A \right\mid \left\mid B \right\mid}$

=(<4,7,2>.<-3,6.6>)/(sqrt(4^2+7^2+2^2)sqrt(3^2+6^2+6^2)

$= \frac{- 12 + 42 + 12}{\sqrt{69} \sqrt{81}}$

$= \frac{42}{\left(\sqrt{69}\right) .9} = \frac{14}{3 \sqrt{69}}$

$= {\cos}^{-} 1 \left(\frac{14}{3 \sqrt{69}}\right) = {55.81}^{\circ}$