Question

Let F = (xy^2) ax + yx^2 ay, F is a not a conservative vector.

(a) True

(b) False

I got this question by my school principal while I was bunking the class.

Origin of the question is Gradient of a Function and Conservative Field topic in section Vector Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (b) False

The best I can explain: Q = xy^2 and P = yx^2

\(\frac{∂P}{∂y} = 2xy\) and \(\frac{∂Q}{∂x} = 2xy \)

Since, both are equal, F is a conservative vector.