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QUESTION 1 a) Evaluate the line integral F. dr in terms of a where F = cos yi + rj+ ye*k and C is the line segments from A (7,0,0) to B (27,™,7). b) Show the force field F(x, y, z) = (x²y + In(y2))i+ + y cos(2z) ) j+ – y² sin(2z) ) k 3 is a conservative field and find its potential function. Using this poten- tial function or otherwise, evaluate the work needed to move an object along line segments from point (0, 1, 1) to point (2, 2, 3), then to point (3, 1, 1), using force F.

QUESTION 1 a) Evaluate the line integral F. dr in terms of a where F = cos yi + rj+ ye*k and C is the line segments from A (7,0,0) to B (27,™,7). b) Show the force field F(x, y, z) = (x²y + In(y2))i+ + y cos(2z) ) j+ – y² sin(2z) ) k 3 is a conservative field and find its potential function. Using this poten- tial function or otherwise, evaluate the work needed to move an object along line segments from point (0, 1, 1) to point (2, 2, 3), then to point (3, 1, 1), using force F.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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QUESTION 1 a) Evaluate the line integral F. dr in terms of T where F = cos yi + xj + ye²¨k and C is the line segments from A (7,0,0) to B (27, 7, ). b) Show the force field F(x, y, z) = (x²y + In(yz)) i+ 3 + y cos(2z) ) j+ - y² sin(2z) ) k is a conservative field and find its potential function. Using this poten- tial function or otherwise, evaluate the work needed to move an object along line segments from point (0, 1, 1) to point (2, 2, 3), then to point (3, 1, 1), using force F.
Transcribed Image Text:QUESTION 1 a) Evaluate the line integral F. dr in terms of T where F = cos yi + xj + ye²¨k and C is the line segments from A (7,0,0) to B (27, 7, ). b) Show the force field F(x, y, z) = (x²y + In(yz)) i+ 3 + y cos(2z) ) j+ - y² sin(2z) ) k is a conservative field and find its potential function. Using this poten- tial function or otherwise, evaluate the work needed to move an object along line segments from point (0, 1, 1) to point (2, 2, 3), then to point (3, 1, 1), using force F.
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