Question

If for a plane, the intercepts on the co-ordinate axes are 8, 4, 4, then the length of the perpendicular from the origin to the plane is ______

Options

• `8/3`

• `3/8`

• 3

• `4/3`

Answer 1

If for a plane, the intercepts on the co-ordinate axes are 8, 4, 4, then the length of the perpendicular from the origin to the plane is `underline(8/3)`.

Explanation:

The equation of the plane is `x/8 + y/4 + z/4 = 1`

i.e., x + 2y + 2z = 8

∴ The length of the perpendicular from origin to the plane is 

d = `|(-8)/sqrt(1 + 4 + 4)| = 8/3`