Question

The foot of the perpendicular drawn from the origin to a plane is the point (1, –3, 1). What is the intercept cut on the x-axis by the plane?

Options

• 1

• 3

• `sqrt(11)`

• 11

Answer 1

11

Explanation:

Equation of plane passing through (1, –3, 1) and whose normal (1, –3, 1) is

1(x – 1) – 3 (y + 3) + 1 (z – 1) = 0

`\implies` x – 3y + z – 11 = 0

`\implies x/11 - y/(11//3) + z/11` = 0

The above plane intercept the x-axis at 11.