If the sum of the squares of the distance of the point P ( x , y , z ) from the co-ordinate axes is 242 , then the distance of the point P from the origin is _______ units.

Step-by-step solution

Distance from the origin for point P(x,y,z) is given by D = x^2 + y^2 + z^2 . The sum of squares of distances from coordinate axes is: d_x^2 + d_y^2 + d_z^2 = (y^2 + z^2) + (x^2 + z^2) + (x^2 + y^2) = 2x^2 + 2y^2 + 2z^2 Given this sum equals 242: 2(x^2 + y^2 + z^2) = 242 x^2 + y^2 + z^2 = 121 Substituting into the distance formula: D = 121 = 11 The distance from the origin is 11 units .