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

19/9

9/19

19/8

8/19

2. A vector with magnitude one is called

Unit vector

Constant vector

Null vector

Zero vector

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

2 – dimensional space

None of these

One – dimensional

3 – dimensional space

4. The vector quantity in the following is

Energy

Angular acceleration

Temperature

Distance

5. A vector of magnitude zero is called

Null vector

Position vector

None of these

Free vector

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

√2

7. The scalar quantity in the following is

Pressure

Acceleration

Force

Velocity

8. 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/6

π/4

π/2

π/3

9. The vector quantity in the following is

Impulse

Energy

Distance

Temperature

10. The unit vector along z-axis is

None of these

k̂

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

√3

12. The scalar quantity in the following is

Velocity

Time

Force

Displacement

13. An example of scalar quantity is

Energy

Force

Velocity

Acceleration

14. An example of scalar quantity is

Force

Power

Velocity

Acceleration

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

Constant

Scalar

Variable

Vector

16. Which is not a vector

Displacement

Electrified intensity

Weight

Density

17. 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

18. An example of vector quantity is

Work

Energy

Power

Force

19. 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

20. The conic is a parabola if

e < 1

e = 1

None of these

e > 1

21. An example of scalar quantity is

Kinetic energy

Weight

Acceleration

Force

22. The scalar quantity in the following is

Velocity

Torque

Force

Speed

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

24.

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

√41

½ √17

½ √14

Page 2 of 2

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

27. 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

28.

29. The magnitude of a vector can never be

None of these

Negative

Positive

Zero

30. 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)

5/√17 (– i – 3j – 10k)

6/√17 (– i + 3j – 10k)

31.

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

None of these

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

Nappes

Branches

Directrices

Vertices

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

35. The perpendicular bisector of any chord of a circle

None of these

Passes through the center of the circle

May or may not pass through the center of the circle

Does not pass through the center of the circle

36. 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

37.

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

a + b + c = 0

Both b and c

a = b = c

a = b + c

39.

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

√74

√89

√76

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

200

√450

√50

√150

42. [k – i, i – j, j – k] = ?

-1

43. The scalar quantity in the following is

Density

Displacement

Velocity

Force

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

Focal axis

Conjugate axis

Major axis

Minor axis

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

√2/3

2/3

√3/2

None of these

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

45°

30°

90°

60°

47. The direction cosines of y-axis are

1, 1, 1

0, 0, 1

0, 1, 0

1, 0, 0

48. An example of vector quantity is

Acceleration

Energy

Work

Power

49. 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 st. line

An ellipse

A circle

50. 3j . k x i

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.
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