Question

Equation of the plane perpendicular to the line `x/1 = y/2 = z/3` and passing through the point (2, 3, 4) is ______

Options

• 2x + 3y + z = 17

• x + 2y + 3z = 9

• 3x + 2y + z = 16

• x + 2y + 3z = 20

Answer 1

Equation of the plane perpendicular to the line `x/1 = y/2 = z/3` and passing through the point (2, 3, 4) is x + 2y + 3z = 20.

Explanation:

The d.r.s. of the line are 1, 2, 3.

The line is perpendicular to the plane.

∴ The d.r.s. of the plane are 1, 2, 3.

∴ The equation of plane passing through (2, 3, 4) is

a(x - 2) + b(y - 3) + c(z - 4) = 0

⇒ 1(x - 2) + 2(y - 3) + 3(z - 4) = 0

⇒ x + 2y + 3z = 20