Vector Calculus - 7


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20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Vector Calculus - 7

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Vector Calculus - 7 - Question 1

A vector   is said to be irrotational vector, if

Vector Calculus - 7 - Question 2

The plane containing principal, normal and binormal is called

Vector Calculus - 7 - Question 3

 Maximum value of directional derivative of f= x2yz at the point (1, 4,1) is

Vector Calculus - 7 - Question 4

 If V is the volume enclosed by surface S and  =  then is

Vector Calculus - 7 - Question 5

If C is a smooth curve in R3 from (–1, 0, 1) to (1, 1, –1), then the value of is

Detailed Solution for Vector Calculus - 7 - Question 5


Vector Calculus - 7 - Question 6

  where P is a vector, is equal to

Vector Calculus - 7 - Question 7

if and  be the set of orthonormal unit vectors, then  is

Vector Calculus - 7 - Question 8

Stoke’s theorem is

Detailed Solution for Vector Calculus - 7 - Question 8

Correct Answer :- D

Explanation : The Stoke’s theorem states that “the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the particular vector function around that surface.”

Stokes theorem says that ∫F·dr = ∬curl(F)·n ds.

Vector Calculus - 7 - Question 9

The relation between the line integral and the surface integral is

Vector Calculus - 7 - Question 10

The divergence of the vector field

Vector Calculus - 7 - Question 11

If Φ(x, y, z) = 3x2y - y3z then the value of grad Φ at the point (1,- 2 ,- 1 ) is

Vector Calculus - 7 - Question 12

If Φ is a differentiable scalar point function, then the value of curl grad Φ is

Vector Calculus - 7 - Question 13

If  then  is

Vector Calculus - 7 - Question 14

A particle moves along the curve Acceleration of the particle in the direction of the motion is

Vector Calculus - 7 - Question 15

Using stokes' theorem evaluate the line integral, where L is the intersection of x2 + y2 + z2 = 1 and x + y = 0 traversed in the clockwise direction when viewed from the point (1, 1, 0)

Detailed Solution for Vector Calculus - 7 - Question 15

By stoke’s theorem
where L is the intersection of x2 + y2 + z2 = 1 and x + y = 0.


The outward unit normal vector

Vector Calculus - 7 - Question 16

Gauss’s divergence theorem can be written a

Detailed Solution for Vector Calculus - 7 - Question 16

The divergence theorem states that the surface integral of the normal component of a vector point function “F” over a closed surface “S” is equal to the volume integral of the divergence of F⃗  taken over the volume “V” enclosed by the surface S. Thus, the divergence theorem is symbolically denoted as :

Vector Calculus - 7 - Question 17

Let is a solution of the Laplace equation then the vector field is 

Detailed Solution for Vector Calculus - 7 - Question 17


 

⇒ Divergence is non-zero and curl is zero,
Hence is not solenoidal but irrotational.

Vector Calculus - 7 - Question 18

Let  be a vector field.
Q. The value of div  is

Detailed Solution for Vector Calculus - 7 - Question 18

 Given that

Therefore, 

Vector Calculus - 7 - Question 19

Let  be a vector field.
Q. The value of curl  is

Detailed Solution for Vector Calculus - 7 - Question 19

 Given that


Vector Calculus - 7 - Question 20

Let  and 
Q. The value of  is

Detailed Solution for Vector Calculus - 7 - Question 20

Given that

and 
Therefore, 

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