Question

How do you compute the dot product to find the magnitude of `u=12i-16j`?

Answer 1

`abs vec u = 20`

Explanation:

you should dot it against itself

by definition `vec u * vec v = abs vec u abs vec v cos psi`

if `vec v = vec u` then `psi = 0` and so `vec u * vec u = abs vec u abs vec u cos 0 = (abs vec u)^ \color{red}{2}`

so `<12, -16> * <12, -16 > = (12)(12) + (-16)(-16) = 400= (abs vec u)^ \color{red}{2}`

so `abs vec u = sqrt 400 = 20`