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10 Nov 2019
Vector field F = M(x, y)i + N(x, y)j or F = M{x, y, z)i + N(x, y, z)j + P(x, y, z)k Position vector = xi + yj or = xi + yj + z k Distance function or Show that F = grad(xy)/||grad(xy)|| is a gradient of some function f(x, y) and then find the potential function f(x, y). Let F( ) = k/rn , where n is appositive integer, k is a constant, and = xi +yj +zk Show F( ) is a gradient vector field. Find the potential function f(x, y, z) such that f = F, if n = 2 ; n 2.
Vector field F = M(x, y)i + N(x, y)j or F = M{x, y, z)i + N(x, y, z)j + P(x, y, z)k Position vector = xi + yj or = xi + yj + z k Distance function or Show that F = grad(xy)/||grad(xy)|| is a gradient of some function f(x, y) and then find the potential function f(x, y). Let F( ) = k/rn , where n is appositive integer, k is a constant, and = xi +yj +zk Show F( ) is a gradient vector field. Find the potential function f(x, y, z) such that f = F, if n = 2 ; n 2.