Question

What is the dot product of two vectors that are perpendicular?

Answer 1

The dot of two vectors is given by the sum of its correspondent coordinates multiplied. In mathematical notation:
let `v = [v_(1), v_(2), ... , v_(n)]` and `u = [u_(1), u_(2), ... , u_(n)]`,
Dot product:
`v*u =`
`sum v_(i).u_(i) = (v_(1).u_(1)) + (v_(2).u_(2)) + ... + (v_(n).u_(n))`

and angle between vectors:
`cos(theta) =(v*u)/(|v||u|)`

Since the angle between two perpendicular vectors is `pi/2`, and it's cosine equals 0:
`(v*u)/(|v||u|) = 0 :. v*u = 0`

Hope it helps.