Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4>
Can someone explain how to do this?

Answer 1

Use the dot product relation:


`\mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta`

where
`\theta` is the angle between
`\mathbf u` and
`\mathbf v`.

You have


`\mathbf u\cdot\mathbf v=6*7+(-1)*(-4)=46`

`\|\mathbf u\|=√(6^2+(-1)^2)=√(37)`

`\|\mathbf v\|=√(7^2+(-4)^2)=√(65)`

So, the angle is given by


`\cos\theta=(46)/(√(37)√(65))\implies \theta\approx20.3^\circ`