Answer to Question #195646 in Differential Geometry | Topology for Fatowore Samson

Question

If G⃗=〖5t〗2i+tj−t3k and

F⃗=sinti–costj, what is d/dt(G×F⃗) ?

Answer 1

$\hat{G}=-2i+tj-3tk \\ \hat{F}=sin t i+cos t j$

$\hat{G}\times \hat{F}=\begin{vmatrix} i &j &k\\-2&t&-3t\\sint &cost &0\end{vmatrix}$

$=i(0+3tcost)-j(0+3tsint)+k(-2cost +tsint)\\[9pt]=3tcosti-3tsint j +(tsint-2cost)k$

$\Rightarrow \dfrac{d(\hat{G}\times \hat{F})}{dt}=3(cost-tsint)i-3(sint+tcost)j+(sint+tcost+2sint)k$

$=3(cost-tsint)i-3(sint+tcost)+(3sint+tcost)k$