Product of Two Quaternion Q and R Coursework - 275 Words

Product of Two Quaternion Q and R (Coursework Sample) Content: Product of two quaternion q and rInsert Name HereInstitutional AffiliationDate of SubmissionProduct of two quaternion q and r given that q = 35 + i à ¢ 4j + 3k and r = 4 + 2i + jEvaluating qr and rq;The quaternion equation is given generally in this form;q=q0+iq1 +jq2 +kq3 and r=ro+ir1+jr2+kr3Then the quaternion (Goldman, 2010) product of the two equation i.e. qÃÆ'r can be given by;t=qÃÆ'r=t0+it1+jt2+kt3In the given question;q0 = 35, q1=1, q2=-4, q3=3 and r0=4, r1=2, r2=1, r3=0In order to get the equation for t= qÃÆ'r, then the following equations should be followed;to= ( r0q0- r1 q1- r2 q2- r3 q3)t1= (r0 q1+r1 q0- r2 q3+ r3 q2)t2= (r0 q2+r1 q3+ r2 q0- r3 q1)t3= (r0 q3-r1 q2+ r2 q1- r3 q0)Therefore;t0= (4ÃÆ'35-2ÃÆ'1-1ÃÆ'-4-0ÃÆ'3) =140-2+4=142t1= (4ÃÆ'1+1ÃÆ'35-1ÃÆ'3+0ÃÆ'-4) =4+35-3=36t2= (4ÃÆ'-4+2ÃÆ'3+1ÃÆ'35-0ÃÆ'1) =-16+6+35=25t3= (4ÃÆ'3-2ÃÆ'-4+1ÃÆ'1-0ÃÆ'35) =12+8+1=21Thus, substituting the values of t0, t1, t2 and t3 in t the product qr is obtained as;qr=142+36i+25j+25kThen rq can be obtained by finding the correspondent t0, t1, t2 and t3 as;to= ( q0 r0- q1 r1- q2 r2 - q3 r3) = (35ÃÆ'4-1ÃÆ'2--4ÃÆ'&...