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

Nappes

Branches

Vertices

Directrices

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

3. The unit vector along z-axis is

None of these

k̂

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

√74

√89

√76

5. The conic is a parabola if

e < 1

e = 1

None of these

e > 1

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

√150

√450

√50

200

7. The scalar quantity in the following is

Torque

Speed

Velocity

Force

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

10. A vector with magnitude one is called

Unit vector

Constant vector

Zero vector

Null vector

11. An example of scalar quantity is

Force

Acceleration

Velocity

Energy

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

√2

13. [k – i, i – j, j – k] = ?

-1

14. The scalar quantity in the following is

Velocity

Acceleration

Pressure

Force

15. An example of scalar quantity is

Force

Kinetic energy

Acceleration

Weight

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

None of these

17. The direction cosines of y-axis are

1, 1, 1

0, 0, 1

1, 0, 0

0, 1, 0

18. 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

A parabola

An ellipse

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

√290

√297

√279

20. A vector of magnitude zero is called

Null vector

Position vector

Free vector

None of these

21.

22.

23. An example of vector quantity is

Work

Force

Power

Energy

24. The scalar quantity in the following is

Velocity

Displacement

Force

Density

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

½ √14

√41

½ √17

Page 2 of 2

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

√3

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

√3/2

2/3

None of these

√2/3

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/3

π/4

π/6

π/2

29. 3j . k x i

30.

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

2 – dimensional space

3 – dimensional space

One – dimensional

None of these

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

Conjugate axis

Focal axis

Major axis

Minor axis

33. The scalar quantity in the following is

Force

Displacement

Time

Velocity

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

Variable

Scalar

Vector

Constant

35. 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

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

5/√17 (– i + 3j – 10k)

5/√17 (– i – 3j – 10k)

5/√110 (– i – 3j – 10k)

6/√17 (– i + 3j – 10k)

37. The perpendicular bisector of any chord of a circle

May or may not pass through the center of the circle

Passes through the center of the circle

None of these

Does not pass through the center of the circle

38. 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

39. 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

40. The magnitude of a vector can never be

Positive

Negative

Zero

None of these

41. The vector quantity in the following is

Angular acceleration

Distance

Energy

Temperature

42. Which is not a vector

Density

Electrified intensity

Displacement

Weight

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

9/19

19/8

8/19

19/9

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

60°

45°

90°

30°

45. An example of scalar quantity is

Velocity

Force

Acceleration

Power

46. a x b = b x c = c x a if

a + b + c = 0

a = b + c

Both b and c

a = b = c

47. The vector quantity in the following is

Energy

Temperature

Impulse

Distance

48. An example of vector quantity is

Energy

Power

Acceleration

Work

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

50.

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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