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- 01. Find the directional derivative of p = x²z + 2xy? + yz? at (1, 2,-1) in the direction of vector (2i + 3j – 4k)Use the gradient vector to find the equation of the tangent plane to the surface x? + y? - at the point (2,2,4). Write your answer in the form Ax + By + Cz = D.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 = (x - y, z + y + 9, z) and the net is decribed by the equation y = V1-x - z, y 2 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) V. dS =
- 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 + 9, z?) and the net is decribed by the equation y = V1 - x² – z7, y > 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.) v · dS = 10n IncorrectEx.: Find the directional derivative of the function f(x, y) = x'y* + x*y* at the point (1,1) in the direction of the vector (4,3).