Question

Given the vectors `u=<2,2>`, `v=<-3,4>`, and `w=<1,-2>`, how do you find `(v*u)-(w*v)`?

Answer 1

`(vec v * vec u) - (vec w * vec v) = 13`

Explanation:

Inner Product Definition
If `vecu = <<(u_1, u_2)>>`, and `vecv = <<(v_1, v_2)>>`, then the inner product (or dot product), a scaler quantity, is given by:
`vecu * vecv = u_1v_1 + u_2v_2`
=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+

So with, `vecu=<<2,2>>`, and `vecv=<<-3,4>>`, and `vecw=<<1,-2>>` we get:

`(vec v * vec u) - (vec w * vec v) = { (-3)(2) + (4)(2) } - { (1)(-3) + (-2)(4) }`
`:. (vec v * vec u) - (vec w * vec v) = {-6 + 8 } - {-3 -8 }`
`:. (vec v * vec u) - (vec w * vec v) = 2 - {-11 }`
`:. (vec v * vec u) - (vec w * vec v) = 13`