Please show all necessary steps!

5 Rotating a point using quaternions Given a quaternion q = a+ib+Jc+ kd, its conjugate is obtained changing the sign of all its imaginary coefficients, i.e., the conjugate is q-a-ib-je-kd. Let us now assume that q = a+ib+jc-kd is a unit quaternion representing a given rotation and that p [Pa 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 quaternion q,-0+Pz1 + pyJ +Pek. 2. compute the quaternion q, = qqpq. Let q, = a't ib'tjd + kd. Then the rotated point is the imaginary coefficients 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 quaternion q = 0.837+0.2240.483j +0.12%, Moreover, verify algebraically that q' always has a' equal to 0