Question 11.21: Find the product of the quaternions p = { p/p4 } = { j/1 } p...

\hat{ p } \otimes \hat{ q } =\left\{\frac{p_4 q +q_4 p + p \times q }{p_4 q_4- p \cdot q }\right\}

=\left\{\frac{\overbrace{1 \cdot(0.5 \hat{i}+0.5 \hat{j}+0.75 \hat{k})}^{0.5 \hat{i}+0.5 \hat{j}+0.75 \hat{k}}+\overbrace{1 \cdot \hat{j}}^{\hat{j}}+\overbrace{\hat{j} \times(0.5 \hat{i}+0.5 \hat{j}+0.75 \hat{k})}^{- 0.5 \hat{k}+0.75 \hat{i}}}{\underbrace{1 \cdot 1}_1-\underbrace{\hat{ j } \cdot(0.5 \hat{ i }+0.5 \hat{ j }+0.75 \hat{ k })}_{0.5}}\right\}

=\left\{\frac{(0.5+0.75) \hat{ i }+(0.5+1.0) \hat{ j }+(0.75-0.5) \hat{ k }}{0.5}\right\}

or

\widehat{ p } \otimes \widehat{ q }=\left\{\frac{1.25 \hat{ i }+1.5 \hat{ j }+0.25 \hat{ k }}{0.5}\right\}