Suppose that in a certain region of space the electric potential V is given by the function V (x, y, z) = 5x2 −3xy + xyz a) Determine the rate of change of the potential at P = (3,4,5) in the direction of the vector v = (1, −1, 1). b) In what direction does V change faster in P? c) What is the maximum rate of change of V in P?
Suppose that in a certain region of space the electric potential V is given by the function V (x, y, z) = 5x2 −3xy + xyz a) Determine the rate of change of the potential at P = (3,4,5) in the direction of the vector v = (1, −1, 1). b) In what direction does V change faster in P? c) What is the maximum rate of change of V in P?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.4: Applications
Problem 8EQ
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Suppose that in a certain region of space the electric potential V is given by the function V (x, y, z) = 5x2 −3xy + xyz
a) Determine the rate of change of the potential at P = (3,4,5) in the direction of the
b) In what direction does V change faster in P?
c) What is the maximum rate of change of V in P?
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