The equation of the plane passing through the point (1,2,1) and perpendicular to the planes x + 2y + 2z - 7 = 0 and 3x + 3y + 2z - 5 = 0 is

Step-by-step solution

Let the normal vector to the required plane be n . Since the required plane is perpendicular to the given planes, its normal vector is perpendicular to the normal vectors of the given planes, n ₁ = i + 2 j + 2 k and n ₂ = 3 i + 3 j + 2 k . n = n ₁ n ₂ = vmatrix i & j & k 1 & 2 & 2 3 & 3 & 2 vmatrix n = i (4 - 6) - j (2 - 6) + k (3 - 6) = -2 i + 4 j - 3 k The equation of the plane passing through (1, 2, 1) with normal vector n is: -2(x - 1) + 4(y - 2) - 3(z - 1) = 0 -2x + 2 + 4y - 8 - 3z + 3 = 0 -2x + 4y - 3z - 3 =