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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
![](https://gs-question-images.grdp.co/1456378075770182.png)
Question 3
For the scalar field
u =
the magnitude of the gradient at the point (1, 3) is :
u =
![](https://gs-question-images.grdp.co/1459162056712335.png)
Question 4
Given a vector field
![](https://gradeup-question-images.grdp.co/equations/1577429612283.png)
![](https://gradeup-question-images.grdp.co/equations/1577429612283.png)
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:
![](https://gradeup-question-images.grdp.co/liveData/PROJ49923/1606733081380697.png)
Question 6
If
then curl
at (1, -1, 1) is
![](https://gradeup-question-images.grdp.co/liveData/PROJ11516/15146237149508100.png)
![](https://gradeup-question-images.grdp.co/liveData/PROJ11516/151462371569245.png)
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
![](https://gradeup-question-images.grdp.co/liveData/PROJ461/147393945912779.png)
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Oct 29ESE & GATE EC