Question

State whether the given equation is a conservative vector.

(a) ax + xy^3 ay

(b) True

(c) False

I have been asked this question by my school principal while I was bunking the class.

My doubt is from Gradient of a Function and Conservative Field in portion Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (b) True

To explain: P = x^3 y and Q = xy^3

\(\frac{∂P}{∂y} = x^3\) and \(\frac{∂Q}{∂x}= y^3 \)

Now since they aren’t equal, the vector is not a conservative vector or field.