Question

Projection vector of `vec"a"` on `vec"b"` is ______.

Options

• `((vec"a"*vec"b")/|vec"b"|^2)vec"b"`

• `(vec"a"*vec"b")/|vec"b"|`

• `(vec"a"*vec"b")/|vec"a"|`

• `((vec"a"*vec"b")/|vec"a"|^2)vec"b"`

Answer 1

Projection vector of `vec"a"` on `vec"b"` is `((vec"a"*vec"b")/|vec"b"|^2)vec"b"`.

Explanation:

Let `vec"a"` and `vec"b"` be two vectors represented by `vec"OA"` and `vec"OB"` respectively.

Now `vec"a"*vec"b" = |vec"a"||vec"b"| cos theta`

= `|vec"b"|(|vec"a"|costheta)`

= `|vec"b"|("OA" cos theta)`

= `|vec"b"|("OL")`

⇒ OL = `(vec"a" * vec"b")/|vec"b"|`

⇒ Projection of vector `vec"a"` on `vec"b" = (vec"a"*vec"b"  vec"b")/(|vec"b"|  |vec"b"|)`

= `(vec"a"*vec"b")/|vec"b"|^2 vec"b"`