7. (a) (5 points) Use the properties of determinant to prove that a b c b c a c a b = (a + b + c)(ab + bc + ca − a 2 − b 2 − c 2 ). (b) (4 points) Use the result in part (a) to calculate the volume of parallelepiped with adjacent edges represented by the vectors u = (2, 3, 5), v = (3, 5, 2), and w = (5, 2, 3). (Your solution should clearly reflect the use of part (a), to receive any credit.)