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Mathematics Vectors Chapter Online Test

Maan AliLast Updated: October 15, 2025

Start your preparation for Mathematics Vectors Chapter Online Test. This online test contains important MCQs from past papers. Attempting this test will help you prepare for Annual Exams and Entry Tests. Read the questions carefully and select the correct option below to see your result.

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

Null vector

Position vector

None of these

Free vector

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

90°

45°

60°

30°

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

√76

√74

√89

4. 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

√845/2

√184

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

9/19

19/9

8/19

19/8

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

√2

7. The direction cosines of y-axis are

1, 0, 0

0, 0, 1

0, 1, 0

1, 1, 1

8. 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

10.

11.

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

None of these

√2/3

2/3

√3/2

13. The scalar quantity in the following is

Velocity

Speed

Force

Torque

14. An example of scalar quantity is

Acceleration

Force

Kinetic energy

Weight

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

√3

16.

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

Scalar

Constant

Vector

Variable

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

½ √17

½ √14

√41

19. The conic is a parabola if

None of these

e = 1

e > 1

e < 1

20. The scalar quantity in the following is

Density

Force

Velocity

Displacement

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

200

√50

√150

√450

22. The vector quantity in the following is

Distance

Energy

Temperature

Angular acceleration

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

6/√17 (– i + 3j – 10k)

5/√110 (– i – 3j – 10k)

5/√17 (– i + 3j – 10k)

5/√17 (– i – 3j – 10k)

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

√3/2

1/√2

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

Nappes

Branches

Directrices

Vertices

Page 2 of 2

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

27. An example of scalar quantity is

Force

Power

Acceleration

Velocity

28. 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/4

π/3

π/2

π/6

29. The scalar quantity in the following is

Displacement

Velocity

Time

Force

30. The scalar quantity in the following is

Velocity

Acceleration

Pressure

Force

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

√279

√297

√290

32. An example of scalar quantity is

Force

Velocity

Energy

Acceleration

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

34. An example of vector quantity is

Work

Power

Force

Energy

35. 3j . k x i

36. Which is not a vector

Density

Displacement

Electrified intensity

Weight

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

One – dimensional

2 – dimensional space

3 – dimensional space

None of these

38. a x b = b x c = c x a if

a = b + c

Both b and c

a + b + c = 0

a = b = c

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

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

Focal axis

Minor axis

Conjugate axis

Major axis

41. The vector quantity in the following is

Temperature

Energy

Impulse

Distance

42. [k – i, i – j, j – k] = ?

-1

43.

44. A vector with magnitude one is called

Zero vector

Null vector

Unit vector

Constant vector

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

A st. line

A circle

An ellipse

A parabola

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

None of these

47. The magnitude of a vector can never be

Positive

Zero

Negative

None of these

48. The perpendicular bisector of any chord of a circle

Passes through the center of the circle

Does not pass through the center of the circle

None of these

May or may not pass through the center of the circle

49. The unit vector along z-axis is

None of these

k̂

50. An example of vector quantity is

Work

Energy

Acceleration

Power

How to Score High in Mathematics Vectors Chapter Online Test?

Mastering scientific subjects requires conceptual clarity.

Key Preparation Tips:

Concepts First: Ensure you understand the underlying theories before attempting the MCQs.
Time Management: Attempt this online quiz multiple times to improve your speed.

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