Question

Given vector `vecA=2hati + 1hatj` and vector `vecB=3hatj`, how do you find the component of `vecA` in the direction of `vecB`?

Answer 1

Please read the vector projection reference and then please read the explanation.

Explanation:

Compute unit vector in the direction of `vecB`:

`hatB = vecB/(|vecB|)`

`|vecB|= sqrt(0^2+3^2)`

`|vecB|= 3`

`hatB = (3hatj)/3`

`hatB = 1hatj`

Let `vecA_B =` the projection of `vecA` in the direction of `vecB`

`vecA_B = (vecA*vecB)/|vecB|(hatB)`

`vecA*vecB = (2)(0)+(1)(3) = 3`

`vecA_B = (3)/3(hatj)`

`vecA_B = hatj`

The would be more instructional, if `vecB` had a non-zero `hati` component but I hope that this helps.