Find the gradient of the following scalar fields and evaluate the gradient at the specified point.

(a) V(x, y, z) = 10xyz – 2x²z at P(–1, 4, 3)

(b) U(p, Φ, z) = 2p sin Φ + pz at Q(2, 90°, –1)

(c) W(r, θ, Φ) = 4 / r sin θ cos Φ at R(1, π/6, π/2)
sin

Transcribed Image Text:

(a) V(x, y, z) = 10xyz - 2x²z at P(-1, 4, 3) (b) Up, 0, 2) = 2p sin + pz at Q(2, 90°, -1) 4 (c) W(r, 0, 0) cos at R(1, π/6, π/2) sin