Question

The projection of vector `vec"a" = 2hat"i" - hat"j" + hat"k"` along `vec"b" = hat"i" + 2hat"j" + 2hat"k"` is ______.

Options

• `2/3`

• `1/3`

• 2

• `sqrt(6)`

Answer 1

The projection of vector `vec"a" = 2hat"i" - hat"j" + hat"k"` along `vec"b" = hat"i" + 2hat"j" + 2hat"k"` is `2/3`.

Explanation:

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

`(vec"a"*vec"b")/|vec"b"| =  ((2hat"i" - hat"j" + hat"k")*(hat"i" + 2hat"j" + 2hat"k"))/sqrt(1 + 4 + 4)`

= `2/3`.