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Problems on vector calculus || Achievers Quiz 1

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Question 1

For a scalar function F(x,y,z,) = x2 + 3y2 + 2z2, the gradient at the point P (3,2,1) is

Question 2

Divergence of the three–dimensional radial vector field is

Question 3

For the scalar field
u = the magnitude of the gradient at the point (1, 3) is :

Question 4

Given a vector field

If the vector field  is solenoidal, then the value of k will be

Question 5

A vector is given by  The divergence of vector at x = 1 is:

Question 6

If then curl at (1, -1, 1) is

Question 7

F(x, y) = (x2 + xy). It’s line integral over the straight line from (x, y) = (0, 2) to (x, y) = (2, 0) evaluates to
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Oct 29ESE & GATE EC