Question

$\sf \red{ Question:- }$For the following vector field F, decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, ▽ f = F) with f(0, 0) = 0.
‏‏‎ ‎
F (x, y) = (-14x - 2y)i + (-2x + 14y)j
[\tex]\sf \red{ Note :- }[/tex]
• Answer it correctly.
• Please don't spam.
• Need full explanation.
• Don't give any irrelevant answer.
━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 1

Answer:

$| | |..226y { \frac{ = - \div \geqslant \leqslant 1 {4866}^{?} \times \frac{?}{?} }{?} }^{2} | | |$

Answer 2

GIVEN :-

A vector field F (x, y) = (-14x - 2y)i + (-2x + 14y)j .

To Find :-

• Whether this field is conservative or not.

Concept

• A field is called conservative if it is path independent. The curl of such field will be zero. That is ▽ X F = 0. In other words, it can be said that a field  will be conservative if it can be written as gradiant of a scalar field. In my solution, i have used this approach. I tried to find a scalar field whose gradiant is the given field.