vector and tensor analysis mcqs with answers

This set of Vector and tensor analysis Multiple Choice Questions & Answers (MCQs) focuses on all outlines of vector and tensor analysis. All Vector and tensor analysis questions are very compulsory and also these mcqs have worth value for all kinds of preparations and tests.

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vector and tensor analysis mcqs with answers

Note: correct answers is with dots

1. Two non zero vectors a and b are perpendicular if and only if

A) a . b = 1

B) a . b = 0

C) a × b = 1

D) a × b = 0.

B) a . b = 0

Differential Equation Questions & Solutions (Separable Method)
2. Find non negative a if |ai + (a+1)j+2k|=3

A) 0

B) -1

C) 2

D) -2

E) 1

3. Find vector whose magnitude is 4 and parallel to 2i -3j +6k.

A) (8/7, 12/7, 24/7)

B) (- 8/7, 12/7, -24/7)

C) (8/7, -12/7, 24/7)

D) (-8/7, -12/7, -24/7)

C) (8/7, -12/7, 24/7)

4. If u= 2i + 3j +4k, v= -i +3j-k and w= I +6j +zk represents the sides of a triangle. What is value of z?

A) 1

B) 2

C) 3

D) 4

C) 3

5. i . i =

A) 0

B) 1

C) i

D) j

B) 1

6. j . k =

A) 0

B) 1

C) i

D) j

A) 0

Hilbert Pace Notes
7. Which of the following triples can be the direction angles of a single vector.

A) 45° ,45°, 60°

B) 30° ,45°, 60°

C) 45° ,60°, 60°

D) None of these

C) 45° ,60°, 60°

8. Find PQ if P= (2,1,5) and Q= (1,3,1)

A) (1,2,4)

B) (-1,-2,-4)

C) (1,-2,4)

D) (-1,2,-4)

9. If u= 2i + 3j + k and v= 4i+6j+2k then u+2v is

A) (6,9,3)

B) (10,15,5)

C) (-2,3,-1)

D) (-6,9,3)

Viscus Fluids Notes

B) (10,15,5)

10. A vector is said to be unit vector if magnitude of a vector is

A) 0

B) -1

C) 2

D) -2

E) 1

11. Projection of B on A is

A) A.B/A

B) A.B/B

C) A.B/AB

D) A.B

A) A.B/A

12. Projection of vector u= ai+ bj+ ck along i is

A) a

B) c

C) b

D) a+b

A) a

13. The angle between the vectors 2i+ 3j+k and 2i-j-k is

A) ㄫ/6

B) ㄫ/4

C) ㄫ/2

D) ㄫ

C) ㄫ/2

14. If the vectors 2ai+j-k and i+aj+4k are perpendicular to each other then the value of a is

A) 3

B) 1/3

C) 2/3

D) 4/3

15. k × i =

A) 0

B) j

C) -j

D) 1

B) j

16. If A and B are parallel vectors then A × B =

A) 0

B) 1

C) -1

D) 2

A) 0

17. The work done when the point of application of the force 3i-j moves in a straight line from the point (2,1) to the point (6,3) is

A) 5 units

B) 10 units

C) 15 units

D) 22 units

B) 10 units

18. (i-j).(j-k)×(k-j)=

A) 1

B) 0

C) i-k

D) j-k

B) 0

19. j . k × i =

A) i

B) j

C) 1

D) k

C) 1

20. [a b c] equals

A) 1

B) 0

C) a

D) b

A) 1

21. a × b= 0 and a . b= 0 then

A) a and b are parallel

B) a and b are perpendicular

C) either a=0 or b=0

D) both a and b are non zero

C) either a=0 or b=0

22. If A and B are opposite directed then A B=

A) AB

B) -AB

C) ABsinθ

D) ABtanθ

B) -AB

23. i . k equals

A) j

B) i

C) 1

D) 0

24. If A and B have same directed then A B=

A) AB

B) -AB

C) ABsinθ

D) ABtanθ

A) AB

25. The work done by a force F through a displacement d is

A) Fdsecθ

B) Fdsinθ

C) F.d

D) Fdtanθ

C) F.d

26. A constant force F acting on a body, displaces it from A to B. The work done by F is equal to

A) F.AB

B) F× AB

C) -F× AB

D) -F.AB

A) F.AB

27. Name of the angle between two non zero vectors a and b is

A). a . b

B).

$\frac{|a||b|}{a.b}$

$\frac{a.b}{|a||b|}$

$\frac{a\times b}{|a||b|}$

28. A unit vector is a vector whose magnitude is

A) 0

B) 1

C) 2

D) Not defined

B) 1

29. Find the value of [k, i, j]

A) 0

B) 1

C) 2

D) 3

B) 1

30. Find projection of u= 3i+ j- k on v= -2i- j+ k is

$\frac{8}{\sqrt{6}}$

$-\frac{8}{\sqrt{6}}$

$-\frac{1}{\sqrt{2}}$

$\frac{1}{\sqrt{2}}$

Solve this please

31. A . B is

A) vector quantity

B) scalar quantity

C) anti commutative

D) neither vector nor scalar

B) scalar quantity

32. A . B is

A) vector quantity

B) scalar quantity

C) anti commutative

D) neither vector nor scalar

B) scalar quantity

33. Scalar quantity in the following is

A) force

B) displacement

C) velocity

D) temperature

34. The vector quantity in the following is

A) distance

B) temperature

C) energy

D) angular acceleration

35. Unit vector along y axis is

A) i

B) j

C) k

D) none

B) j

36. If v is a vector for which v.i=0, v.j=0, v.k=0 then value of v will be

A) 0

B) i

C) j

D) k

A) 0

37. If a= (2,1,-1), b=(1,-1,1) then a × b is

A) (0,3,3)

B) (0,-3,3)

C) (0,-3,-3)

D) (0,3,-3)

C) (0,-3,-3)

38. Let a= i + j , b= i - j then a × b is

A) -2i

B) -2j

C) -2k

D) -2

C) -2k

39. Unit vector containing a and b where a= (2,-6,-3) and b= (4,3,-1) is

A) 1/7 (3,2,6)

B) 1/7 (3,-2,6)

C) 1/7 (3,2,-6)

D) 1/7 (3,2,6)

B) 1/7 (3,-2,6)

40. The volume of parallelpiped for which u= 3i + 2k , v= i + 2j +k, w= -j+ 4k

A) 13

B) 6

C) 17

D) 25

41. Value of 2i ×2j .k is

A) 4

B) 8

C) 9

D) 1

A) 4

42. Value of 3j . k × i is

A) 1

B) 2

C) 3

D) 4

C) 3

43. Value of [k i j] is

A) 1

B) 0

C) 2

D) k

A) 1

44. Value of [i i k] is

A) 1

B) 0

C) 2

D) k

B) 0

45. u . (v × w) + v . (w × u) + w . (u × v) =

A) 3 u . (v × w)

B) 3 v . (w × u)

C) 3 w . (u × v)

D) None of these

A) 3 u . (v × w)

46. Volume of tetrahedron of vertices (2,1,8), (3,2,9), (2,1,4), (3,3,10) is

A) 3/2

B) 2/3

C) 8/3

D) 3/8

B) 2/3

47. If the point at which a constant force f is equal to 4 i +3j + 5k is applied to an object moves from P(3,1,-2) to Q(2,4,6). Then work done is

A) 36

B) 45

C) 28

D) 12

B) 45

48. A force F= 4i - 3k, passes through the point A(2,-2,5). The moment of force F about the point B(1,-3,1) is

A) (3,4,7)

B) (4,-19, 3)

C) (3,-19,4)

D) (-3,19,-4)

49. Sum of the vectors AB and CD of four points A(1,-1), B(2,0), C(-1,3), D(-2,2)

A) 0

B) 1

C) 2

D) 3

A) 0

50. The vector whose magnitude is 2 and is parallel to -i +j + k is

A) ( 2/√3, 2/√3,2/√3)

B) ( -2/√3, 2/√3,2/√3)

C) ( 2/√3, -2/√3,2/√3)

D) ( 2/√3, 2/√3,-2/√3)

B) ( -2/√3, 2/√3,2/√3)

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vector and tensor analysis mcqs with answers