Question

if `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`, , then express `vecb` in the form of `vecb = vec(b_1) + vec(b_2)`, where `vec(b_1)`  is parallel to `veca` and `vec(b_2)` is perpendicular to `veca`

Answer 1

Let `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`

Now, `vec(b_1)` and `vec(b_2)` are two vectors such that

`vecb = vec(b_1) + vec(b_2)`

`=> vec(b_2) = vecb - vec(b_1)`  ....(1)

Since `vec(b_1)`is parallel to `veca`, therefore