Question

If a plane has x-intercept l, y-intercept m and z-intercept n, and perpendicular distance of plane from the origin is k, then _______.

Options

• `1/l^2 + 1/"m"^2 + 1/"n"^2 = "k"^2`

• `1/l^2 + 1/"m"^2 + 1/"n"^2 = 1/"k"^2`

• l² + m² + n² = `1/"k"^2`

• l² + m² + n² = k²

Answer 1

`1/l^2 + 1/"m"^2 + 1/"n"^2 = 1/"k"^2`

Explanation:

The intercepts made by the plane are

a, b, c  = l, m, n

∴ The distances of plane from origin is

d = `1/(sqrt(1/"a"^2 + 1/"b"^2 + 1/"c"^2))`

`=> "k" = 1/(sqrt(1/l^2 + 1/"m"^2 + 1/"n"^2))`

`=> 1/l^2 + 1/"m"^2 + 1/"n"^2 = 1/"k"^2`