(a) \(AB=B-A=(3,4,-7)=OC\), and \(CB=B-C=(5,-2,1)=OA\). Thus opposite sides are equal and parallel. Also \(OA\cdot OC=15-8-7=0\), proving the rectangle. (b) Diagonal vectors \(OB=(8,2,-6)\), \(AC=(-2,6,-8)\). Their dot product is 44 and each squared length is 104. Hence \(\theta=\cos^{-1}(44/104)=65.0^\circ\).