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

2. 3j . k x i

3. The scalar quantity in the following is

Force

Acceleration

Velocity

Pressure

4. The scalar quantity in the following is

Velocity

Displacement

Density

Force

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

√297

√290

√279

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

9/19

8/19

19/9

19/8

7. 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

8. An example of scalar quantity is

Velocity

Acceleration

Power

Force

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

None of these

10. The unit vector along z-axis is

None of these

k̂

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

Minor axis

Major axis

Conjugate axis

Focal axis

12.

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

√2

14. Which is not a vector

Weight

Density

Displacement

Electrified intensity

15. 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

16.

17. The magnitude of a vector can never be

Zero

Negative

Positive

None of these

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

19. A vector with magnitude one is called

Null vector

Unit vector

Zero vector

Constant vector

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

21. The scalar quantity in the following is

Speed

Force

Torque

Velocity

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

Directrices

Branches

Nappes

Vertices

23. The perpendicular bisector of any chord of a circle

Does not pass through the center of the circle

May or may not pass through the center of the circle

None of these

Passes through the center of the circle

24.

25. 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

A circle

An ellipse

A st. line

Page 2 of 2

26. An example of scalar quantity is

Force

Weight

Kinetic energy

Acceleration

27. An example of scalar quantity is

Force

Energy

Velocity

Acceleration

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

30°

60°

90°

45°

29. An example of vector quantity is

Work

Energy

Acceleration

Power

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

√3

31. An example of vector quantity is

Energy

Work

Force

Power

32.

33. The vector quantity in the following is

Distance

Temperature

Impulse

Energy

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

200

√150

√450

√50

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

None of these

√3/2

2/3

√2/3

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

Variable

Scalar

Vector

Constant

37. The vector quantity in the following is

Energy

Temperature

Distance

Angular acceleration

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

√74

√76

√89

39. a x b = b x c = c x a if

a + b + c = 0

a = b + c

Both b and c

a = b = c

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

5/√110 (– i – 3j – 10k)

5/√17 (– i – 3j – 10k)

6/√17 (– i + 3j – 10k)

5/√17 (– i + 3j – 10k)

41. The direction cosines of y-axis are

0, 1, 0

0, 0, 1

1, 1, 1

1, 0, 0

42.

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

½ √17

½ √14

√41

44. [k – i, i – j, j – k] = ?

-1

45. 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

46. A vector of magnitude zero is called

None of these

Position vector

Null vector

Free vector

47. The scalar quantity in the following is

Velocity

Time

Displacement

Force

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

None of these

One – dimensional

3 – dimensional space

2 – dimensional space

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

√845/2

√184

√676

50. The conic is a parabola if

None of these

e > 1

e = 1

e < 1

How to Score High in Mathematics Vectors Chapter Online Test?

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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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