Question

The unit vector normal to the plane x + 2y +3z – 6 = 0 is `1/sqrt(14)hat"i" + 2/sqrt(14)hat"j" + 3/sqrt(14)hat"k"`.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Given plane is x + 2y + 3z – 6 = 0

Vector normal to the plane `vec"n" = hat"i" + 2hat"j" + 3hat"k"`

∴ `hat"n" = vec"n"/|vec"n"|`

= `(hat"i" + 2hat"j" + 3hat"k")/sqrt((1)^2 + (2)^2 + (3)^2`

= `1/sqrt(14)hat"i" + 2/sqrt(14)hat"j" + 3/sqrt(14)hat"k"`