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In each of the above problems, the answer is a positive integer. (a) The value of 'a' such that the vector field F(x, y, z) = ev+2z (i + xj + axk) is conservative is (b) The expression [(-2i+ 3k) × (i +23-k)]. (73-4k) equals X (c) Let the tangent plane to 2x2 + 2xy-3z = 1 at the point (1, 1, 1) be given by Ax+By+Cz= 1. Then the value of A + B is (d) Let R be the disk of radius 3 centered at the origin. The value of the integral 1 SRTVE+V² -dA, equals dw (e) If w = x¹4 +y and x + y² = t and 3x + y = t, the value of Ət when y= 2 equals

In each of the above problems, the answer is a positive integer. (a) The value of 'a' such that the vector field F(x, y, z) = ev+2z (i + xj + axk) is conservative is (b) The expression [(-2i+ 3k) × (i +23-k)]. (73-4k) equals X (c) Let the tangent plane to 2x2 + 2xy-3z = 1 at the point (1, 1, 1) be given by Ax+By+Cz= 1. Then the value of A + B is (d) Let R be the disk of radius 3 centered at the origin. The value of the integral 1 SRTVE+V² -dA, equals dw (e) If w = x¹4 +y and x + y² = t and 3x + y = t, the value of Ət when y= 2 equals

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 14P
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In each of the above problems, the answer is a positive integer. (a) The value of 'a' such that the vector field F(x, y, z) = ev+22 (2 + xj + axk) is conservative is (b) The expression [(-2i+ 3k) x (i +23-k)] (73 - 4k) equals (c) Let the tangent plane to 2x² + 2xy - 3z = 1 at the point (1, 1, 1) be given by Ax+By+Cz= 1. Then the value of A + B is (d) Let R be the disk of radius 3 centered at the origin. The value of the integral 1 JATRA dA, TV x² + y² equals dw when y (e) If w = x¹4 +y and x + y² = t and 3x + y = t, the value of Ət 2 equals
Transcribed Image Text:In each of the above problems, the answer is a positive integer. (a) The value of 'a' such that the vector field F(x, y, z) = ev+22 (2 + xj + axk) is conservative is (b) The expression [(-2i+ 3k) x (i +23-k)] (73 - 4k) equals (c) Let the tangent plane to 2x² + 2xy - 3z = 1 at the point (1, 1, 1) be given by Ax+By+Cz= 1. Then the value of A + B is (d) Let R be the disk of radius 3 centered at the origin. The value of the integral 1 JATRA dA, TV x² + y² equals dw when y (e) If w = x¹4 +y and x + y² = t and 3x + y = t, the value of Ət 2 equals
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