Question

What is the angle between vectors u = <5, -2, 4> and v=<4, 6, 2> ? (rounded to the nearest degree)1º359°10°71°

Answer 1

The formula is;

`\begin{gathered} u.v=\lvert{u\lvert{}\rvert v}\rvert cos\theta \\ \end{gathered}`
`\begin{gathered} u.v=5(4)+(-2)(6)+4(2) \\ u.v=16 \end{gathered}`
`\begin{gathered} \lvert{u}\rvert=√((5^2+-2^2+4^2))\text{ } \\ \lvert{u=√(45)}\rvert \end{gathered}`
`\begin{gathered} \lvert{v}\rvert=√(4^2+6^2+2^2) \\ \lvert{v}\rvert=√(56) \end{gathered}`
`16=√(45)X√(56)\text{ }cos\theta\text{ }`
`\cos\theta=(16)/(√(45)X√(56))=(16)/(50.1996)=0.3187`
`\theta=\cos^(-1)(0.3187)=\text{ 71}\degree`

θ = 71°