Question

How do you compute the dot product for `u=i-2j` and `v=-2i+j`?

Answer 1

`:. ulu * ulv = -4`

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=ulhati-2ulhatj`, and `ulv=-2ulhati+ulhatj`

Then the inner product is given by;
`ulu * ulv = (1)(-2) + (-2)(1)`
`:. ulu * ulv = -2 - 2`
`:. ulu * ulv = -4`