The curl of vector field F =x’yi + xyz] + z’yk at the point (0,1, 2) is
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Concept:
We need to recall the concept of curl of a vector field to answer this question.
Curl of a vector field F(x,y,z) = Xi+Yj+Zk is denoted by curl F.
Defined as: curl F =
Given:
The vector field F = xy i +xyz j +zy k
To find:
The curl of vector field at point (0,1,2).
Solution:
On Comparing the given vector field with
F(x,y,z) = Xi+Yj+Zk
we get, X = xy
Y = xyz
Z = zy
Curl of F is given by :
Curl F =
= (z-xy) i - (0-0) j + (yz- x) k
= (z-xy) i + 0 j + (yz- x) k
At point (0,1,2),
Curl F = (2-0×1 ) i +0 j + (1×2 -0) k
= 2 i +0 j + 2k
Hence, curl of the vector field at point (0,1,2) is given by : 2 i +0 j + 2k
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