#### 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`

#### Solution

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

Is there an error in this question or solution?

Solution If `Veca = 2hati - Hatj - 2hatk "And" Vecb = 7hati + 2hatj - 3hatk`, , Then Express `Vecb` in the Form of `Vecb = Vecb_1 + Vecb_2`, Where `Vecb_1` is Parallel to `Veca` and `Vecb_2` is Perpendicular to `Veca` Concept: Types of Vectors.