Question

Determine the angle between the lines y=4x+2 and y=-x+3.

Please explain. Does this have something to do with cosine direction? Please help.

Answer 1

The vector
`v_1=(4,1)` is parallel to the line
`y=4x+2`
and the vector
`v_2(-1,1)` is parallel to the line
`y=-x+3`.
On one hand
`v_1v_2=(-1)4+1^2=-3`.
On the other hand

`v_1v_2=\vert v_1\vert\vert v_2\vert cos\theta\\=√(17)√(2)\cos\theta`

Equating we get
`√(34)\cos\theta=-3`.
so
`\theta=\cos^(-1)(-3)/(√(34))=120\text{ degrees}`