Find the equation of a plane which is at a distance of 3√3 units from the origin and the normal to which is equally inclined with the coordinate axes.

Let and be the angles made by with x, y and z - axes respectively.

It is given that

α = β = γ

cos α = cos β = cos γ

l = m = n, where l, m, n are direction cosines of.

But l² + m² + n² = 1

Or, l² + l² + l² = 1

Or, 3 l² = 1

Or,

Or,

So, l = m = n =

It is given that the length of the perpendicular of the plane from the origin, p =

The normal form of the plane is lx + my + nz = p.