Question

How do you compute the dot product for `<0, 3>*<4, -2>`?

Answer 1

`<< 0,3 >> * << 4,-2 >> = -6`

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`
Inner Product = 0 `hArr` vectors are perpendicular

So, `ulu=3ulhatj`, and `ulv=4ulhati-2ulhatj`

Then the inner product is given by;

`ulu * ulv = << 0,3 >> * << 4,-2 >>`
`" "= (0)(4) + (3)(-2)`
`" "= 0-6`
`" "= -6`