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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
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
where c is the curve x2+y2=1 and z=y2 isQuestion 3
The directional derivative of f (x, y, z) =x2 - y2 +2z2 at 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 _____.
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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Jun 20ESE & GATE EC
