The drawback of angle-axis representation can be overcome by 4- parameter representation, i.e. unit quaternion, defined by Q={n, e) where the scalar 0 0 part is n = cos and vector part by & = [&, &, &] =sin-r. 2 2 a. First prove that: n+&+&+ = 1 b. Next prove that the rotation matrix corresponding to the unit quaternion is given by R(n, e) = [2(n + ) - 1 2(ry + nez) 2(Exez-ney) 2(Exty - nez) 2(n + ) - 2(Eyez+nex) 2(x +ney) 2(Eyz - Nex) 2(n + ) - 1