Product of Two Quaternion Q and R (Coursework Sample)

Product of two quaternion q and r
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Product of two quaternion q and r given that q = 35 + i ‒ 4j + 3k and r = 4 + 2i + j
Evaluating qr and rq;
The quaternion equation is given generally in this form;
q=q0+iq1 +jq2 +kq3 and r=ro+ir1+jr2+kr3
Then the quaternion (Goldman, 2010) product of the two equation i.e. q×r can be given by;
t=q×r=t0+it1+jt2+kt3
In the given question;
q0 = 35, q1=1, q2=-4, q3=3 and r0=4, r1=2, r2=1, r3=0
In order to get the equation for t= q×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= (4×35-2×1-1×-4-0×3) =140-2+4=142
t1= (4×1+1×35-1×3+0×-4) =4+35-3=36
t2= (4×-4+2×3+1×35-0×1) =-16+6+35=25
t3= (4×3-2×-4+1×1-0×35) =12+8+1=21
Thus, substituting the values of t0, t1, t2 and t3 in t the product qr is obtained as;
qr=142+36i+25j+25k
Then rq can be obtained by finding the correspondent t0, t1, t2 and t3 as;
to= ( q0 r0- q1 r1- q2 r2 - q3 r3) = (35×4-1×2--4Ã&...