Question

Find the gradient of a function V if V= xyz.

(a) yz ax + xz ay + xy az

(b) yz ax + xy ay + xz az

(c) yx ax + yz ay + zx az

(d) xyz ax + xy ay + yz az

The question was posed to me in an interview.

The doubt is from Gradient of a Function and Conservative Field topic in chapter Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) yz ax + xz ay + xy az

To elaborate: V = xyz

Gradient of \(V = \frac{∂V}{∂x} a_x + \frac{∂V}{∂y}a_y + \frac{∂V}{∂z}a_z \)

= yz ax + xz ay + xy az