Question

If the projection of `2hat"i"+4hat"j"-2hat"k"` on `hat"i"+ 2hat"j"+alphahat"k"` is zero. Then, the value of α will be ______.

Options

• 1

• 3

• 5

• 9

Answer 1

If the projection of `2hat"i"+4hat"j"-2hat"k"` on `hat"i"+ 2hat"j"+alphahat"k"` is zero. Then, the value of α will be 5.

Explanation:

Here, `vec"a".vec"b"` = 0

∴ `vec"a".vec"b" = (2hat"i"+4hat"j"-2hat"k").(hat"i"+ 2hat"j"+alphahat"k")` = 0

∴ 2 × 1 + 4 × 2 - 2 × α = 0

∴ α = 5