Mathematics Exam  >  Mathematics Questions  >  For the vector fieldWhich of the following is... Start Learning for Free
For the vector field
 Which of the following is/are true?
  • a)
    Vector field  is conservative.
  • b)
     is solenoidal vector field.
  • c)
     is irrotational vector field.
  • d)
     where c is any path from (0,0,1) to 
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
For the vector fieldWhich of the following is/are true?a)Vector fieldi...
For the conservative vector field
curve 
Hence vector field is conservative Vector field and given dine integral is independent from the path. So it is irrotational vector field also.
Now a scalar field such that
dφ = (2xyz2)dx + (x2z2 + zcosyz)dy+(2x2yz + ycosyz)d2
= (2xyz2ds + x2z2dy + 2x2yzdz) + (zcosyzdy + y cos yzdz)
= d(x2yz2) + d (sinyz)
= x2y2+sinyz + C
View all questions of this test
Most Upvoted Answer
For the vector fieldWhich of the following is/are true?a)Vector fieldi...
For the conservative vector field
curve 
Hence vector field is conservative Vector field and given dine integral is independent from the path. So it is irrotational vector field also.
Now a scalar field such that
dφ = (2xyz2)dx + (x2z2 + zcosyz)dy+(2x2yz + ycosyz)d2
= (2xyz2ds + x2z2dy + 2x2yzdz) + (zcosyzdy + y cos yzdz)
= d(x2yz2) + d (sinyz)
= x2y2+sinyz + C
Explore Courses for Mathematics exam
For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer?
Question Description
For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer?.
Solutions for For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer?, a detailed solution for For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? has been provided alongside types of For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice For the vector fieldWhich of the following is/are true?a)Vector fieldis conservative.b)is solenoidal vector field.c)is irrotational vector field.d)where c is any path from (0,0,1) toCorrect answer is option 'A,C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
Explore Courses for Mathematics exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev