Question

Find a.b. a=[p,-p,2p], b=[2q,q,-q]

Answer 1

`a.b = -pq`

Explanation:

We are given the following in the question:

`a=[p,-p,2p], b=[2q,q,-q]`

We have to find the dot product.

Formula:

`a = [x_1,x_2,x_3]\\b = [y_1.y_2,y_3]\\a.b = x_1y_1 + x_2y_2 + x_3y_3`

Putting the corresponding values we get,

`a.b = (p.2q) + (-p.q) + (2p.-q)\\= 2pq-pq-2pq\\=-pq`

`a.b =-pq`