Question

how do i.... Find the angle between each pair of vectors below. (1 point each) a. a = 2x + 3y a = 4x + 2y

Answer 1

Recall that the dot product between two vectors
`\mathbf a` and
`\mathbf b` satisfies

`\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta`

where
`\|\mathbf x\|` denotes the norm of a vector
`\mathbf x`, and
`\theta` is the angle between the two vectors.

So if
`\mathbf a=(2,3)` and
`\mathbf b=(4,2)`, then

`(2,3)\cdot(4,2)=\|(2,3)\|\|(4,2)\|\cos\theta`

`\implies2\cdot4+3\cdot2=√(2^2+3^2)√(4^2+2^2)\cos\theta`

`\implies\cos\theta=(14)/(√(13)√(20))`

`\implies\theta\approx29.7^\circ`