Question

If the foot of perpendicular drawn from the origin to the plane is (3, 2, 1), then the equation of plane is ____________.

Options

• 3x + 2y − z = 12

• 3x − 2y − z = 12

• 3x + 2y − z = 14

• 3x + 2y + z = 14

Answer 1

If the foot of perpendicular drawn from the origin to the plane is (3, 2, 1), then the equation of plane is 3x + 2y + z = 14.

Explanation:

P(3, 2, 1) denotes the perpendicular's foot of a line traced from the starting point to the plane.

∴ OP is perpendicular to the plane.

As a result, the normal to the plane's direction ratio is (3, 2, 1)

Now that the plane has passed through (3, 2, 1)

∴ It equation is 3(x − 3) + 2(y − 2) + 1(z − 1) = 0

3x − 9 + 2y − 4 + z − 1 = 0

3x + 2y + z = 14