Question

Given the coordinates A (5, 7, -2) and B (8, 3, 4) in 3d space, express AB as:

a) a 3x1 column vector b) in the form xi + yj + zk

Answer 1

The vector AB is found by subtracting the coordinates of point B from the coordinates of point A => (8, 3, 4) - (5, 7, - 2)

(8, 3, 4) - (5, 7, - 2) = (3, - 4, 6)

=>

a) a 3 x 1 column =

| 3 |
| -4 |
| 6 |

b) xi + yj + zk

=> 3i - 4j + 6k