Question

If the foot of the perpendicular drawn from the point (0, 0, 0) to the plane is ( 4, - 2, -5) then the equation of the plane is ______.

Options

• 4x + 2y + 5z = - 13

• 4x - 2y - 5z = 45

• 4x + 2y - 5z = 37

• 4x - 2y + 5z = - 5

Answer 1

If the foot of the perpendicular drawn from the point (0, 0, 0) to the plane is (4, - 2, -5) then the equation of the plane is 4x - 2y - 5z = 45.

Explanation:

We have, foot of the perpendicular drawn from the point (0, 0, 0) to the plane is (4, -2, -5).

∴ Direction ratios of normal to the required plane is

(0 - 4, 0 + 2, 0 + 5 i.e -4, 2, 5)

∴ Required equation of plane passing through (4, - 2, 5) is

a(x - x₁) + b(y - y₁) + c(z - z₁) = 0

⇒ (- 4) (x - 4) + (- 2) (y + 2) + (5) (z + 5) = 0

⇒ - 4x + 2y + 5z + 16 + 4 + 25 = 0

⇒ 4x - 2y - 5z = 45