Test: Vector Analysis - 1
10 Questions MCQ Test Topicwise Question Bank for Electrical Engineering | Test: Vector Analysis - 1
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If
φ = xy2z3 then match List-I with List-II and select the correct answer using the codes given below the lists:
φ = xy2z3 then match List-I with List-II and select the correct answer using the codes given below the lists: Here 
Also,
And,
The unit vector 
which points from z = h on the z-axis towards (r, φ, 0) in cylindrical co-ordinates as shown below is given by
which points from z = h on the z-axis towards (r, φ, 0) in cylindrical co-ordinates as shown below is given byLet the unit vector be given by 
Now,
∴ Unit vector,
If the vector V given below is irrotational, then the values of a, b and c will be respectively
Since the given vector is irrotational, therefore curl V = 0 or, 
Since, 
therefore, a = 4, b = 2, and c = -1
Match List-I (Vector Identities) with List-ll. (Equivalent expression) and select the correct answer using the codes given below the lists:
is called “ product of four vectors ”.
is called “vector triple product”.
is called "vector product of four vectors ”.
The vector differential operator, 
in spherical co-ordinate system is given by
Assertion (A): Divergence of a vector function 
at each point gives the rate per unit volume at which the physical entity is issuing from that point.
Reason (R): If some physical entity is generated or absorbed within a certain region of the field, then that region is known as source or sink respectively and if there are no sources or sinks in the field, the net outflow of the incompressible physical entity over any part of the region is zero. However, the net outflow is said to be positive, if the total strength of the sources are greater than the total strength of sink and vice-versa.
Both assertion and reason are true and reason is the correct explanation of assertion. Reason is the physical interpretation of divergence.
is called “vector triple product" which is a correct expression.
The vector 
directed from (2, - 4,1) to (0, -2,0) in Cartesian coordinates is given by
The vector 
is given as
What is the value of 
where 
Here, s is the surface bounded by x = 0, x = 1, y = o, y = 1, z = 0, z =1 and 
are unit vectors along x, yand z axes respectively.
By divergence theorem,
Since, the surface s is bounded by x = 0, 1; y = 0, 1 and z = 0, 1 so, putting the limits, we have
The vector field 
will be irrotational, 
Now,
Hence, 
is irrotationai.
The vector field 
will be solenoidal, 
Here, 
Hence, 
is solenoidal.
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