5 Rotating a point using quaternions Given a quaternion q-atibtjc+kd, its conjugate is obtained changing the sign of a ts imaginary coefficients, i.c., the conjugate is q = a_ib_JC-kd. Let us now assulne that q = a + ib+jc+kd is a unit quaternion representing a given rotation and that p pr Py p is a point in R3. We want to rotate the point p by the rotation defined with the quaternion q. This can be done as follows: 1. from p build a quatornion qp-0+ Pri + pyJ + P:k. 2. colnpute the quaternion q, qqpq. Let q'-a, t ib, + Jd + kd. Then the rotated point is Pr = 1b, d d'r. i.e., it is obtained from the imaginary cofficients of the product. Following the above method, compute the point obtained by rotating the point p 2 1 3 by the rotation associated with the quaterion q 0.8374 0.2240.483 1-0 129 : M(rcover, verify algebraically that q' always has a' equal to 0