Question

The gradient of a scalar field V is a vector that represents both magnitude and the direction of the maximum space rate of increase of V.

(a) True

(b) False

This question was posed to me at a job interview.

My question comes from Gradient of a Function and Conservative Field in division Vector Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (a) True

To elaborate: A gradient operates on a scalar only and gives a vector as a result. This vector has a magnitude and direction. The gradient is found by finding the speed that is by taking the partial differentiation.