Question

If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2), then the equation of plane is `vec"r".(5hat"i" - 3hat"j" - 2hat"k")` = 38.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

The given equation of the plane is `vec"r".(5hat"i" - 3hat"j" - 2hat"k")` = 38

If the foot of the perpendicular to this plane is (5, – 3, – 2)

i.e., `5hat"i" - 3hat"j" - 2hat"k"` then

`(5hat"i" - 3hat"j" - 2hat"k").(5hat"i" - 3hat"j" - 2hat"k")` = 38

⇒ 25 + 9 + 4 = 38

38 = 38 .....(satisfied)