Question

Find the angle between the vectors having direction ratios $(3,4,5)$ and $(4,-3,5)$.

Answer 1

$\begin{array}{c}\cos \theta =\frac{3\left(4\right)+4\left(-3\right)+5\left(5\right)}{\sqrt{9+16+25}\sqrt{16+9+25}}\\ \cos \theta =\frac{25}{50}=\frac{1}{2}\\ \therefore \theta ={60}^{\circ }.\end{array}$