Question

How do you find the angle between the vectors `u=5i+5j` and `v=-8i+8j`?

Answer 1

Angle: `90°`

Explanation:

In order to calculate the angle between two vectors, we have to know that

`cos(theta) = (vecu * vecv)/(||vecu|| ||vecv||)`

`u * v` means the dot product of `u` and `v`, which we can calculate using the formula

`vecu*vecv = u_1 v_1 + u_2 v_2 + ... u_n v_n`

In our case, `vecu = 5hati + 5hatj` and `vecv = -8hati + 8hatj`

`vecu * vecv = 5(-8) + 5(8) = -40 + 40 = 0`

Since the dot product is `0`, we can conclude that `vecu` and `vecv` are perpendicular to each other, so the angle between them would equal `90`.