- #1

thomas49th

- 655

- 0

## Homework Statement

The points A and B have position vectors a = (2,2,1) and b (1,1,-4) respectively relative to an origin O. (im using column notation for shorthand)

Prove that OA is perpendicular to AB

## Homework Equations

## The Attempt at a Solution

To be perpendicular the angle between the lines is 90

using the dot product rule:

vectors a and b should multiply to give cos 90 (which is 0)

AB = (3,3,-3)-(2,2,1) = (1,1,-4)

so:

(2,2,1).(1,1,-4) = (2,2,-4)

NOW WHAT I DONT UNDERSTAND IS why you add the components i,j,k to get 0. I can see 2 + 2 -4 =0, but why do you do this? Why can you do this

Thanks :)