Find the curl of the vector field F = < 5z cos(x), 6z sin(x), 4z > . curl F = 1:2 1'1 k + +
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- Find the curl of the vector fieldF (6y cos(x), 7x sin(y)) curl F =Define two vector functions (t) 9 sin(t)+7 cos(t)] + (t³ - 15) k = = (t) 7 sin(t)+9 cos(t)] + tk = . Compute (t) (t) =Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)
- Find the derivative of the vector functionr(t)=ta×(b+tc) wherea=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and c=⟨−3,−2,−3⟩A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)Calculate the derivative (r × r'), where r = (5t, t²,e¹). dt (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) d (rxr') = (2te',-5e¹,0) dt Incorrect