Question

Find the projection of the vector `hati - hatj` on the vector `hati + hatj`.

Answer 1

Let `veca = hati - hatj`

and `vecb = hati + hatj`

`|vecb| = sqrt(1^2 + 1^2)`

`= sqrt(1 + 1)`

`= sqrt2`

Also, `veca. vecb = (hati - hatj)* (hati + hatj)`

= (1) (1) + (-1) (1)

= 1 - 1

= 0

∴ Projection of `vec a  "on"  vec b = (veca. vecb)/|vecb|`

`= 0/sqrt2`

= 0