[a (a) Given the 3 by 3 matrix A= b a+d a+e b+d b+e for any real values of a, b, c, d, and [c C c+e] e, show that the determinant is |A|=de(ab). (b) For the following three Cartesian equations of planes, P., P, P3: (1) R: x+2y+3z=14 P: 4x+5y+6z=32 P3: 7x+7y+9z=48 [6 marks] Using part (a), put the equations in the matrix form Ax=b and solve the equation to find the coordinates (x,ypp) of the point where the planes intersect. [12 marks] [2 marks] (ii) Determine the perpendicular distance from the origin to plane P3. (c) Calculate the work done when the force F = x+y+zk moves an object along the vector d = n xn, where n, and n denote the normal vectors of the planes P and P respectively. [5 marks]