Question

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

Answer 1

`(3w * v)vec(u) = <<-66,-66>>`

Explanation:

Inner Product Definition
If `ulu = <<(u_1, u_2)>>`, and `ulv = <<(v_1, v_2)>>`, then the inner product (or dot product), a scaler quantity, is given by:

`ulu * ulv = u_1v_1 + u_2v_2`

So, `vec(u)=<<2,2>>`, `vec(v)=<<-3,4>>`, and `vec(w)=<<1,-2>>`

Then the inner product `(3w * v)` is given by;

`3vec(w) * vec(v) = 3<<1,-2>> * <<-3,4>>`
`" "= <<3,-6>> * <<-3,4>>`
`" "= (3)(-3) + (-6)(4)`
`" "= -9 -24`
`" "= -33`

And so the vector `(3w * v)vec(u)` is:

`(3w * v)vec(u) = -17vec(u)`
`" "= -33<<2,2>>`
`" "= <<-66,-66>>`