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Unformatted text preview: + x2 k. (b) 2y i - z 2 j - x2 k Solution: (a) 10. Suppose F is a vector field, and F = (xy 2 + zy + xz 2 ). Let C be the straight line segment from (0, 0, 1) to (1, 1, 2). Evaluate (a) 7 Solution: (a) 11. If F is a conservative vector field, one of the following statements is not necessarily true. Which one is not true? (a)
C C F d r. (b) 0 (c) 3 (d) 5. F dr = 0 for any closed curve C (b) F = 0 (d) F = 0. (c) F = for some scalar function Solution: (d) 12. Let F be a vector field and be a scalar function (both differentiable as required). Then (F) (a) is zero if F is conservative (c) is a scalar quantity Solution: (c) 13. Find a unit vector normal to the surface e2x y+xz 2 = 1 at the point (0, 1, 1). 3i + j 3i + j + k i + 3j + k i + 3j (b) (c) (d) . (a) 10 10 11 11 Solution: (b) 14. Let C be the parabola y = x2 from the point (0, 0) to the point (1, 1). Evaluate
C (b) is a vector quantity (d) is not a meaningful expression. F d r, where F = x i -...
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