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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` - CBSE (Commerce) Class 12 - Mathematics

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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

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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.
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