Suppose that over a certain region in space the electrical potential V is given by V(x, y, z) = 52 - 2ry + xyz (a) Find the rate of change of the potential at P( - 2, 1, -1) in the direction of (3, 1, - 2) Round your answer to three decimals. (b) Find a unit vector in the direction of maximum increase of V at point P( - 2,1, - 1) Round your value(s) to three decimals. (c) What is the maximum rate of change of V at P - 2,1, -1) Round your answer to three decimals.

Question
Suppose that over a certain region in space the electrical potential V is given by
V(x, y, z) = 52 - 2ry + xyz
(a) Find the rate of change of the potential at P( - 2, 1, -1) in the direction of (3, 1, - 2)
Round your answer to three decimals.
(b) Find a unit vector in the direction of maximum increase of V at point P( - 2,1, - 1)
Round your value(s) to three decimals.
(c) What is the maximum rate of change of V at P - 2,1, -1)
Round your answer to three decimals.
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Transcribed Image Text

Suppose that over a certain region in space the electrical potential V is given by V(x, y, z) = 52 - 2ry + xyz (a) Find the rate of change of the potential at P( - 2, 1, -1) in the direction of (3, 1, - 2) Round your answer to three decimals. (b) Find a unit vector in the direction of maximum increase of V at point P( - 2,1, - 1) Round your value(s) to three decimals. (c) What is the maximum rate of change of V at P - 2,1, -1) Round your answer to three decimals.

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