Question

How would I find the angle between vectors `u` & `v` if `u``=``i`+`4j` & `v``=``-i`+`2j`?

Answer 1

I found `40.6^@`

Explanation:

I wold try using the Scalar (dot) Product between them:
We have: either (using the components):
`vecu*vecv=u_xv_x+u_yv_y=(1*-1)+(4*2)=-1+8=7`
or:
`vecu*vecv=|vecu|*|vecv|*cos(theta)`

where `theta` is the angle between the two vectors:

`|vecu|=sqrt(1^2+4^2)=sqrt(17)`
`|vecv|=sqrt((-1)^2+2^2)=sqrt(5)`

Now we can use the two versions together:
`u_xv_x+u_yv_y=|vecu|*|vecv|*cos(theta)`

`7=sqrt(17)sqrt(5)cos(theta)`
`theta=cos^-1(7/(sqrt(17)sqrt(5)))=40.6^@`