Answer to Question #141174 in Calculus for Foysal Mahmud

Question #141174
If u=5t2i+j−t k and v=sinti−costj then, at t=0, ddt(u×v)=
1
Expert's answer
2020-11-01T16:03:57-0500

u "\\times v=\\begin{vmatrix}\n i & j & k \\\\\n 5t^{2} & 1 & -t\\\\\nSint & -Cost & 0 \n\\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



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