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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 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)

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

√89

√74

√76

3. 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

4. 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

5. An example of scalar quantity is

Acceleration

Force

Weight

Kinetic energy

6. An example of scalar quantity is

Power

Force

Velocity

Acceleration

7. The scalar quantity in the following is

Displacement

Velocity

Density

Force

8. An example of scalar quantity is

Velocity

Energy

Acceleration

Force

10. Which is not a vector

Displacement

Weight

Density

Electrified intensity

11. The unit vector along z-axis is

None of these

k̂

12. A vector of magnitude zero is called

None of these

Null vector

Free vector

Position vector

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

Major axis

Minor axis

Conjugate axis

Focal axis

14. 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 parabola

An ellipse

A circle

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

√3

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

½ √17

½ √14

√41

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

60°

45°

90°

30°

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

None of these

19. 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

√676

√184

20. a x b = b x c = c x a if

a + b + c = 0

a = b = c

a = b + c

Both b and c

21.

22. The scalar quantity in the following is

Velocity

Torque

Speed

Force

23. The scalar quantity in the following is

Velocity

Time

Force

Displacement

24. The vector quantity in the following is

Distance

Angular acceleration

Temperature

Energy

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

One – dimensional

None of these

2 – dimensional space

3 – dimensional space

Page 2 of 2

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

√50

√450

200

√150

27. A vector with magnitude one is called

Zero vector

Constant vector

Null vector

Unit vector

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

Vector

Variable

Constant

Scalar

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

9/19

19/8

19/9

8/19

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

31. An example of vector quantity is

Force

Work

Energy

Power

32. 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/3

π/4

π/6

π/2

33.

34.

35. 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

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

Directrices

Vertices

Nappes

Branches

37. The scalar quantity in the following is

Velocity

Pressure

Acceleration

Force

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

√2

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

40. The magnitude of a vector can never be

Zero

Negative

Positive

None of these

41. 3j . k x i

42. 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

43. The direction cosines of y-axis are

0, 0, 1

0, 1, 0

1, 1, 1

1, 0, 0

44.

45. An example of vector quantity is

Work

Power

Acceleration

Energy

46. The conic is a parabola if

e = 1

e < 1

None of these

e > 1

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

48. [k – i, i – j, j – k] = ?

-1

49. The perpendicular bisector of any chord of a circle

May or may not pass through the center of the circle

None of these

Passes through the center of the circle

Does not pass through the center of the circle

50. The vector quantity in the following is

Energy

Temperature

Impulse

Distance

How to Score High in Mathematics Vectors Chapter Online Test?

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Concepts First: Ensure you understand the underlying theories before attempting the MCQs.
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