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4. (- (a) 4 Find the constants a, b, c so that ▼ = (x + 2y + az)i + (bx − 3y − z)j + (4x + cy +2z)k is irrotational. (b) () Show that can be expressed as the gradient of a scalar function. 5. () Find the work done in moving a particle once around a circle C' in the xy-plane, if the circle has center at the origin and radius 3 and if the force field is given by: F(x, y) = (2x − y + z)i + (x + y − 2²)j + (3x − 2y + 4z)k

4. (- (a) 4 Find the constants a, b, c so that ▼ = (x + 2y + az)i + (bx − 3y − z)j + (4x + cy +2z)k is irrotational. (b) () Show that can be expressed as the gradient of a scalar function. 5. () Find the work done in moving a particle once around a circle C' in the xy-plane, if the circle has center at the origin and radius 3 and if the force field is given by: F(x, y) = (2x − y + z)i + (x + y − 2²)j + (3x − 2y + 4z)k

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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4. (- (a) 4 Find the constants a, b, c so that V = (x + 2y + az)i + (bx − 3y − z)j + (4x + cy + 2z)k is irrotational. (b) () Show that can be expressed as the gradient of a scalar function. 5. () Find the work done in moving a particle once around a circle C in the xy-plane, if the circle has center at the origin and radius 3 and if the force field is given by: F(x, y) = (2x − y + z)i + (x + y − z²)j + (3x − 2y + 4z)k
Transcribed Image Text:4. (- (a) 4 Find the constants a, b, c so that V = (x + 2y + az)i + (bx − 3y − z)j + (4x + cy + 2z)k is irrotational. (b) () Show that can be expressed as the gradient of a scalar function. 5. () Find the work done in moving a particle once around a circle C in the xy-plane, if the circle has center at the origin and radius 3 and if the force field is given by: F(x, y) = (2x − y + z)i + (x + y − z²)j + (3x − 2y + 4z)k
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