Let a plane P pass through the point (3, 7, -7) and contain the line x - 2 -3 = y - 3 2 = z + 2 1 . If the distance of the plane P from the origin is d, then d^2 is

Step-by-step solution

The plane contains the line x - 2 -3 = y - 3 2 = z + 2 1 , so it passes through the point B(2, 3, -2) and is parallel to the vector b = -3 i + 2 j + k . The plane also passes through the point A(3, 7, -7) . The vector joining A and B is AB = (2 - 3) i + (3 - 7) j + (-2 - (-7)) k = - i - 4 j + 5 k . The normal vector n to the plane is perpendicular to both b and AB . n = b AB = vmatrix i & j & k -3 & 2 & 1 -1 & -4 & 5 vmatrix n = i (10 + 4) - j (-15 + 1) + k (12 + 2) = 14 i + 14 j + 14 k . The direction ratios of th