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# GATE EC 2022: Engineering Mathematics | Vector Calculus

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Question 1

If the vector function is irrotational, then the values of the constants k1, k2 and k3 respectively, are

Question 2

The value of integral where c is the curve x2+y2=1 and z=y2 is

Question 3

The directional derivative of f (x, y, z) =x2 - y2 +2zat P (1, 2, 3) in the direction of line PQ, where Q = (5, 0, 4), is ________.

Question 4

A vector field D = exists inside a cylindrical region enclosed by the surfaces r = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on S is _____.

Question 5

Let ∇.(fv) = x2y + y2z + z2x , where f and v are scalar and vector fields respectively. If v = yi + zj + xk, then v.∇f is

Question 6

It is given that the vector function ( 2xy + z3 )i + x2j + 3xz2kis irrotational. Then find scalar potential function corresponding to it
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