Math Problem Solver

. Suppose that over a certain region of space the electrical potential

V x y z ( , , )

is given by

2 V x y z x xy xyz ( , , ) 5 3 , = − + .

(a) Find the rate of change of the potential at

P(3,4,5)

in the direction of the vector

v i j k = + − .

(b) In which direction does

V

change most rapidly at

P

?