Engineering Mathematics
Calculus
Vector Calculus
Questions mapped to Vector Calculus under Calculus.
22
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IncorrectGiven that , the integral over the unit sphere centered at the origin evaluates to
(Round off to one decimal place)
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Sign in to UnlockLet . The rate of change of the real valued function,
at the origin in the direction of the point is __________ (round off to the nearest integer).
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Sign in to UnlockConsider a vector , where represent unit vectors along the coordinate axes respectively. The directional derivative of the function at the point in the direction of is
0
7
21
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Sign in to UnlockThe closed curve shown in the figure is described by , where ;
. The magnitude of the line integral of the vector field around the closed curve is __________ (Round off to 2 decimal places).
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Sign in to UnlockLet be a region in the first quadrant of the plane enclosed by a closed curve C considered in counter-clockwise direction. Which of the following expressions does not represent the area of the region ?
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Sign in to UnlockLet and be unit vectors along and directions, respectively. A vector function is given by .
The line integral of the above function, along the curve , which follows the parabola as shown below is __________. (rounded off to 2 decimal places).
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Sign in to UnlockIf , the value of line integral . dr evaluated over contour C formed by the segments is ______________.
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Sign in to UnlockIf then div(uA) at (1, 1, 1) is ____________.
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Sign in to UnlockThe value of the directional derivative of the functionat the point in the direction of the vectoris
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Sign in to UnlockThe value of the line integral along a path joining the origin (0, 0, 0) and the point (1, 1, 1) is
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Sign in to UnlockThe line integral of the vector field along a path from (0, 0, 0) to (1, 1, 1) parametrized by is ______________.
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Sign in to UnlockConsider a function , where r is the distance from the origin and is the unit vector is the radial direction, the divergence of this function over a sphere of radius R, which includes the origin, is
0
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Sign in to UnlockThe line integral of function F=yzi, in the counter clockwise direction, along the circle at z = 1 is
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Sign in to UnlockLet , where f and v are scalar and vector fields respectively. If , then is
2xy + 2yz + 2zx
x + y + z
0
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Sign in to UnlockThe curl of the gradient of the scalar field defined by is
0
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Sign in to UnlockGiven a vector field , the line integral ∫F.dl evaluated along a segment on the x-axis from x=1 to x=2 is
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Sign in to UnlockThe two vectors [1, 1, 1] and , where , are
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Sign in to UnlockDivergence of the three-dimensional radial vector field is
3
1/r
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Sign in to UnlockIt's line integral over the straight line from evaluates to
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Sign in to UnlockDivergence of the vector field
is
None of these
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Sign in to UnlockA surface S(x, y) = 2x + 5y − 3 is integrated once over a path consisting of the points that satisfy. The integral evaluates to
0
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Sign in to UnlockFor the scalar field , the magnitude of the gradient at the point (1,3) is:
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