Question

A unit vector `hata` makes equal but acute angles on the coordinate axes. The projection of the vector `hata` on the vector `vecb = 5hati + 7hatj - hatk` is ______.

Options

• `11/15`

• `11/(5sqrt(3))`

• `4/5`

• `3/(5sqrt(3))`

Answer 1

A unit vector `hata` makes equal but acute angles on the coordinate axes. The projection of the vector `hata` on the vector `vecb = 5hati + 7hatj - hatk` is `underlinebb(11/15)`.

Explanation:

Let θ be the equal acute angle with coordinate axes.

`\implies` l = m = n = cos θ and l² + m² + n² = 1

`\implies` 3l² = 1

`\implies` l = `1/sqrt(3)`

So `veca = (1/sqrt(3) hati + 1/sqrt(3) hatj + 1/sqrt(3) hatk)`

and projection on b = `5hati + 7hatj - hatk` is given by

`(veca. vecb)/|b| = ((5 + 7 - 1)/sqrt(3))/sqrt(25 + 49 + 1)`

= `11/sqrt(225)`

= `11/15`.