Question

If `veca = << 2,4,-1 >>`, `vecb = << 6,1,2 >>` and `vecc = veca - vecb`, what is the angle between `veca` and `vecc`?

Answer 1

`1.306~~74.83^@`

Explanation:

`vecc = veca-vecb`

`= <2,4,-1> - <6,1,2 >`

`= <-4,3,-3>`

Using that for two vectors `vecv` and `vecw` forming an angle `theta`, we have `cos(theta)=(vecv*vecw)/(||vecv||*||vecw||)`, we can find the angle `gamma` between `veca` and `vecc` by

`cos(gamma) = (veca*vecc)/(||veca||*||vecc||)`

`=(<2,4,-1> * <-4,3,-3>)/(sqrt(2^2+4^2+(-1)^2)*sqrt((-4)^2+3^2+(-3)^2)`

`=(2(-4)+4(3)+(-1)(-3))/(sqrt(21)*sqrt(34)`

`=7/sqrt(714)`

`=>gamma = arccos(7/sqrt(714))~~1.306`