# What is the angle between <4 , 7 , -4 >  and  < 5 , 2 , 3 > ?

$\theta = {66.64}^{0}$
Let vecu =<4,7, -4> and vecv =<5,2,3> ; theta be the angle between them ; then we know cos theta= (vecu*vecv)/(||vecu||*||vecv||)=((4.5)+(7*2)+(-4*3))/(sqrt(4^2+7^2+(-4)^2)* (sqrt(5^2+2^2+3^2)) $= \frac{22}{\sqrt{81} \cdot \sqrt{38}} = \frac{22}{9 \cdot \sqrt{38}} = 0.3965 \therefore \theta = {\cos}^{-} 1 \left(0.3965\right) = {66.64}^{0}$[Ans]