Mathematics Vectors Chapter Online Test

Maan AliLast Updated: October 15, 2025

Important Math Vectors Question and Answer

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Vector Practice Test Online With Explanation

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Page 1 of 2

1. A vector of magnitude zero is called

Free vector

Position vector

Null vector

None of these

2. An example of scalar quantity is

Kinetic energy

Force

Acceleration

Weight

3. The vector quantity in the following is

Temperature

Distance

Angular acceleration

Energy

4. A vector of magnitude 5 and perpendicular to a = i + 3j-k and b = 3i –j is

6/√17 (– i + 3j – 10k)

5/√17 (– i + 3j – 10k)

5/√17 (– i – 3j – 10k)

5/√110 (– i – 3j – 10k)

5. The cosine of the angle between the vector a and b where a = I + 2j – k , b = -I + j – 2k is

1/√2

√3/2

6. $Math 21.05$

7. The magnitude of a vector can never be

Zero

Negative

None of these

Positive

8. An example of vector quantity is

Force

Power

Work

Energy

9. The direction cosines of y-axis are

1, 1, 1

1, 0, 0

0, 1, 0

0, 0, 1

10. The value of 3j. (^k + ^i) = ?

None of these

11. The scalar quantity in the following is

Torque

Velocity

Speed

Force

12. $Math 21.03$

13. $Math 21.02$

14. The perimeter a triangle formed by 3i + 4j + 5k, 4i -3j -5k and 7i + j is

√450

√50

200

√150

15. The projection of a = i – 2j + k along b = 4i – 4j + 7k is

19/9

19/8

8/19

9/19

16. The vector quantity in the following is

Distance

Temperature

Impulse

Energy

17. If u = -I + 2j + 4k and V = 2i –j + 4k are two adjacent sides of a parallelogram then area of parallelogram is

√290

√297

√279

18. The scalar quantity in the following is

Pressure

Force

Acceleration

Velocity

19. The two different parts of the hyperbola are called its

Vertices

Nappes

Directrices

Branches

20. A force f = 2i + 4j - 2k is applied at P(2, 3, -1) its moment about A(1, 0, 3) is as coterminous edges is

21. An example of vector quantity is

Acceleration

Energy

Work

Power

22. $Math 21.01$

23. If V = [2, 1, 3] and w = [–1, 4, 0] then |V – 2w| =

√74

√76

√89

24. a x b = b x c = c x a if

a = b = c

a + b + c = 0

a = b + c

Both b and c

25. The set R³ = {x, y, z): x, y, zε R} is called the

2 – dimensional space

One – dimensional

3 – dimensional space

None of these

Page 2 of 2

26. The volume of the tetrahedron that has a = I + 2j + 3k, b = 3i + j + 2k and c = 2i + 3j + k as its vertices is

27. An example of scalar quantity is

Energy

Velocity

Acceleration

Force

28. $Math 21.04$

29. [k – i, i – j, j – k] = ?

-1

30. The scalar quantity in the following is

Force

Displacement

Velocity

Time

31. A vector with magnitude one is called

Zero vector

Unit vector

Null vector

Constant vector

32. If the vector 2i + 4j – 7k and 2i + 6j + xk are perpendicular then x = ?

33. The conic is a parabola if

e < 1

e > 1

e = 1

None of these

34. Which is not a vector

Density

Displacement

Weight

Electrified intensity

35. 3j . k x i

36. The scalar quantity in the following is

Displacement

Force

Velocity

Density

37. If a and b are two non – zero vectors the component of b along a is

√2/3

√3/2

None of these

2/3

38. The unit vector along z-axis is

k̂

None of these

39. If the distance of a point on the ellipse x²/6 + y²/2 = 1 from the center is 2, then the eccentric angle is

π/2

π/6

π/4

π/3

40. The modulus of the sum of three mutually perpendicular unit vectors is

√3

41. The physical quantity which is completely specified by its magnitude only is called

Scalar

Constant

Vector

Variable

42. If the angle between two vectors with magnitude 6 and 2 is 60° then their scalar product is

43. The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is

A parabola

An ellipse

A st. line

A circle

44. The line through the center and perpendicular to the transverse axis is called the

Major axis

Conjugate axis

Minor axis

Focal axis

45. An example of scalar quantity is

Force

Power

Velocity

Acceleration

46. The area enclosed by the triangle ABC whose vertices are A(1, 2, -3) B (0,0,0) and c (2, 4, 7) is

√676

√184

√845/2

47. If 1 and 1 are x and y –components of a vector, then its angle with x – axis is

90°

30°

60°

45°

48. If u = [3, -4], then {u} = ?

√2

49. The area of a parallelogram whose adjacent sides are represented by 3i k and I + 2j is

½ √14

√41

½ √17

50. The perpendicular bisector of any chord of a circle

None of these

Does not pass through the center of the circle

Passes through the center of the circle

May or may not pass through the center of the circle

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