If the line, x - 1 2 = y + 1 3 = z - 2 4 meets the plane, x + 2 y + 3 z = 15 at a point P , then the distance of P from the origin is,

Step-by-step solution

Let x - 1 2 = y + 1 3 = z - 2 4 = λ Let, coordinate of any point on line is P = 2 λ + 1 ,   3 λ - 1 ,   4 λ + 2 If P is intersection point of plane & line then P will lie on plane x + 2 y + 3 z = 15 ∴   2 λ + 1 + 2 3 λ - 1 + 3 4 λ + 2 = 15 ⇒ λ = 1 2 ∴   P = 2 × 1 2 + 1 ,   3 × 1 2 - 1 ,   4 × 1 2 + 2 = 2 ,   1 2 ,   4 The distance of a point x 1 ,   y 1 ,   z 1 from origin O is x 1 2 + y 1 2 +