Question: Given that a = 3i + j + k, b = 2i - j + 2k, and c = i + j + k, find
(a) a vector normal to the plane containing the vectors a + (a · b)b and c and,
(b) explain why the normal to a plane containing the vectors a and b and the normal to a plane containing the vectors (a · b)a and (b · c)b are parallel.