Question

What is the projection of vector `hati - hatj` on the vector `hati + hatj`.

Options

• 0

• 1

• 2

• 3

Answer 1

0

Explanation:

Let `veca = hati - hatj` and `vecb = hati + hatj`

Then, protection of `veca` on `vecb = (veca * vecb)/|vecb|`  ......(1)

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

= `(1) (1) + (-1) (1) = 1 - 1` = 0

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

From (1), we have,

∴ Projection of `hati - hatj` on the vector `hati + hatj`

= `((hati - hatj) * (hati + hatj))/(|hati + hatj|) = 0/sqrt(2)` = 0