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GATE EC 2021 Set 1 — Question 27

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NAT+1 / -0EasyGradient, Divergence & CurlVector CalculusEngineering Mathematics

Engineering Mathematics → Vector Calculus → Gradient, Divergence & Curl

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Question

Consider the vector field F=ax(4y−c1z)+ay(4x+2z)+az(2y+z)\mathbf{F} = \mathbf{a}_x(4y - c_1z) + \mathbf{a}_y(4x + 2z) + \mathbf{a}_z(2y + z) in a rectangular coordinate system (x,y,z)(x, y, z) with unit vectors ax,ay\mathbf{a}_x, \mathbf{a}_y, and az\mathbf{a}_z. If the field F\mathbf{F} is irrotational (conservative), then the constant c1c_1 (in integer) is ________.
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