Question

Find the angle between \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Short answer

The angle is \(32^\circ\).

Step-by-step solution

Given Information

The given vectors are \(u=<2,4,-1>\) and \(v=<0,-3,2>\).

Let the angle between \(u\) and \(v\) be \(\theta\).

\(\theta=\cos^{-1}\frac{u\cdot v}{|u||v|}\)

Find the angle between two vector

\(\theta=\cos^{-1}\frac{<2,4,-1>\cdot <0,-3,2>}{\sqrt{2^2+4^2+(-1)^2}\sqrt{0^2+(-3)^2+2^2}}\)

\(=\cos^{-1}\frac{0-12-2}{\sqrt{4+16+1}\sqrt{9+4}}\)

\(=\cos^{-1}\frac{-14}{\sqrt{21}\sqrt{13}}\)

\(=\cos^{-1}\frac{0-12-2}{\sqrt{4+16+1}\sqrt{9+4}}\)

\(\approx32^\circ\)