Question

If u=5t2i+j−t k and v=sinti−costj then, at t=0, ddt(u×v)=

Answer 1

u $\times v=\begin{vmatrix} i & j & k \\ 5t^{2} & 1 & -t\\ Sint & -Cost & 0 \end{vmatrix}$ =i*(-t Cost)-j*(tSint)+k*(-5t$^{2}$ Cost-Sint)

=-[i*(tCost)+j*(tSint)+k*(5t$^{2}$ Cost+Sint)]

$\dfrac{d}{dt}(u\times v)$ =-[i*(Cost-tSint)+j*(Sint-tCost)+k(10tCost-5t$^{2}$ Sint+Cost)]

At t=0, the above value becomes=-i-k