Question

Show that: Dt[r1(t)r2(t)]=r1'(t)r2(t)+r1(t)r2'(t)

Answer 1

\[Dt[\vec{r_{1}}(t) \times \vec{r_{2}}(t)] = \vec{r_1}'(t) \times \vec{r_2}(t) + \vec{r_1}(t) \times \vec{r_2}'(t)\]. Without letting the above vectors be in the form \[<x_{i}(t), y_{i}(t), z_{i}(t)> (i=1,2)\]

Answer 2

Anyone? Any takers?