Question

Which of the following vector fields are conservative? (i) F(x, y) = (9y8 +3) i + (8x8y' +7) j (ii) F(x,y) = (8ye8x + cos 3ji + (e8x + 3x sin 3jj (iii) F(x,y)-7y2e7xyİ + (7 +xy) e7xyj (A) all of them (B) (iii) only (C) (i) and (ii) only (D) (i) and (iii) only (E) none of them (F) (ii) and (iii) only (G) (ii) only (H) (i) only st Save Submit Problem #1 for Grading Problem 1 a) Attempt #2 Attempt #3 Attempt #1 Your Answer: 0/2x Your Mark: Find the work done by the following force field in moving an object from P(6,-8) to 2(7,-6), along any path st Save Submit Problem #2 for Grading Problem 1b) Attempt #1 Attempt #2 | Attempt #3 Attempt #4 Attempt #5 Your Answer: Your Mark:

Please answer part a and b :)

Answer 1

Definition of a conservative vector field: Given a vector field F(x,y) Mi +Nj, where M and N have continuous partial derivatives on an open disk R, would be conservative, if and only if, nM ON Here M and N satisfy the condition of having continuous partial derivatives on open disk R ax

Here also, the condition of continuity of partai derivatives of M and N is satisfied, but aM ON Hence, the given F(x,y) is not conservative The correct Option to choose from, is thus (E)

F(x,y) is thus a conservative force field. Since the force field is conservative, we can choose any path. We can choosethe straight line joining P and Q. Its wquation can be written as OY 7-6 82-6) títRt-aj' γ㈦: 6çtSF în parametric form this would be ON

Jb 15 2 24 t2124 1296 a

니 IS118321- 83 Lo 32

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