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

√3

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

√2

3. 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

4. [k – i, i – j, j – k] = ?

-1

5. 3j . k x i

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

5/√17 (– i – 3j – 10k)

6/√17 (– i + 3j – 10k)

5/√17 (– i + 3j – 10k)

5/√110 (– i – 3j – 10k)

7. A vector of magnitude zero is called

Null vector

None of these

Position vector

Free vector

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

One – dimensional

None of these

2 – dimensional space

3 – dimensional space

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

19/9

9/19

8/19

19/8

11. An example of scalar quantity is

Force

Weight

Acceleration

Kinetic energy

12. The direction cosines of y-axis are

0, 0, 1

0, 1, 0

1, 1, 1

1, 0, 0

13. A vector with magnitude one is called

Unit vector

Null vector

Zero vector

Constant vector

14. 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/3

π/6

π/4

15. The scalar quantity in the following is

Displacement

Time

Force

Velocity

16. The unit vector along z-axis is

None of these

k̂

17.

18. The conic is a parabola if

e = 1

None of these

e < 1

e > 1

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

Variable

Constant

Scalar

Vector

20. The scalar quantity in the following is

Acceleration

Force

Pressure

Velocity

21. The vector quantity in the following is

Distance

Angular acceleration

Energy

Temperature

22.

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

Major axis

Minor axis

Focal axis

Conjugate axis

24. The magnitude of a vector can never be

Positive

Negative

None of these

Zero

25. Which is not a vector

Electrified intensity

Density

Weight

Displacement

Page 2 of 2

26. The scalar quantity in the following is

Density

Velocity

Displacement

Force

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

√74

√76

√89

28. The perpendicular bisector of any chord of a circle

May or may not pass through the center of the circle

Does not pass through the center of the circle

Passes through the center of the circle

None of these

29. 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

30. An example of scalar quantity is

Force

Energy

Acceleration

Velocity

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

Directrices

Nappes

Branches

Vertices

32. a x b = b x c = c x a if

a = b + c

Both b and c

a + b + c = 0

a = b = c

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

√184

√845/2

√676

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

90°

30°

45°

60°

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

200

√450

√150

√50

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

√2/3

None of these

√3/2

2/3

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

A circle

An ellipse

A st. line

A parabola

38.

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

½ √14

√41

½ √17

40. An example of scalar quantity is

Force

Velocity

Acceleration

Power

41. An example of vector quantity is

Work

Energy

Power

Acceleration

42. An example of vector quantity is

Energy

Work

Force

Power

43.

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

45. The scalar quantity in the following is

Torque

Speed

Force

Velocity

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

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

None of these

48. The vector quantity in the following is

Impulse

Distance

Temperature

Energy

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

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

√279

√290

√297

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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