Vector Analysis-Gradient, Divergence and Curl in Cartesian and Cylindrical Coordinates [IFS (Forest Services) Mathematics]: Questions 1 - 8 of 14
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Question 1
Appeared in Year: 2011 (IAS)
Describe in Detail Subjective▾
If be the potion vector of a point find the values of for which the vector is –
Irrotational
Solenoidal (15 marks)
EditExplanation
- Let, given position vector is,
… (266 more equations) …
Question 2
Appeared in Year: 2015 (IAS)
Describe in Detail Subjective▾
A vector field is given by
Verify that the field is irrotational or not. Find the Scalar potential. (CS Paper 1)
EditExplanation
We have
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Question 3
Appeared in Year: 2011 (IAS)
Describe in Detail Subjective▾
Examine whether the vectors are coplanar, where are the scalar functions defined by:
And (Paper I)
EditExplanation
- Given
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Question 4
Appeared in Year: 2010 (IAS)
Write in Short Short Answer▾
Prove that
Where f is a scalar function. (Paper I)
EditQuestion 5
Appeared in Year: 2009 (IAS)
Describe in Detail Subjective▾
Find the directional derivative of –
(i)
(ii) in the direction of (Paper 1)
EditExplanation
(i) Here
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Question 6
Appeared in Year: 2007 (IAS)
Describe in Detail Subjective▾
If , find the value of n in order that may be (i) solenoidal, (ii) irrational (Paper 1)
EditExplanation
Here
(i)
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Question 7
Explanation
Grad
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Question 8
Appeared in Year: 2020 (IAS)
Describe in Detail Subjective▾
For what value of is the vector field
irrational? Hence express as the gradient of a scalar function
(Paper 1)
EditExplanation
The vector is irrational if
We have
… (205 more equations) …