Given, the plane is at a distance of 5√3 units form the origin and the normal to the plane is equally inclined with the co - ordinates axis, so, its direction cosines are \(\cfrac{1}{\sqrt3},\cfrac{1}{\sqrt3},\cfrac{1}{\sqrt3}\)
We know, for a plane having direction cosines as l, m and n, and p be the distance of the plane from the origin, the equation of the plane is given as, lx + my + nz = p
So, in this problem, the equation of the required equation of the plane is given by,
Hence, the equation of the required plane which is at a distance of 5√3 units from the origin and the normal to which is equally inclined to co - ordinate axes is x + y + z = 15.
