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ECAT Mathematics Vectors Chapter Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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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1. An example of vector quantity is

Acceleration

Work

Power

Energy

2. 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

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

√2

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

2 – dimensional space

None of these

One – dimensional

3 – dimensional space

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

½ √14

√41

½ √17

6. A vector of magnitude zero is called

None of these

Position vector

Free vector

Null vector

7. An example of vector quantity is

Force

Energy

Work

Power

8. The scalar quantity in the following is

Force

Pressure

Acceleration

Velocity

9. Which is not a vector

Density

Electrified intensity

Weight

Displacement

10.

11.

12. The direction cosines of y-axis are

0, 0, 1

0, 1, 0

1, 0, 0

1, 1, 1

13. An example of scalar quantity is

Force

Acceleration

Kinetic energy

Weight

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

45°

90°

60°

30°

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

None of these

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

Variable

Constant

Scalar

Vector

17. The vector quantity in the following is

Impulse

Energy

Temperature

Distance

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

Vertices

Directrices

Branches

Nappes

19. The unit vector along z-axis is

k̂

None of these

20. The vector quantity in the following is

Energy

Distance

Temperature

Angular acceleration

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

√450

200

√150

√50

22. The magnitude of a vector can never be

Positive

None of these

Zero

Negative

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

√279

√297

√290

24. The scalar quantity in the following is

Force

Time

Velocity

Displacement

25.

Page 2 of 2

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

27. The scalar quantity in the following is

Displacement

Velocity

Force

Density

28. 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)

29. 3j . k x i

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

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

An ellipse

A circle

A st. line

A parabola

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

a = b + c

a = b = c

a + b + c = 0

Both b and c

33.

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

√76

√89

√74

35. 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

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

√3

37. An example of scalar quantity is

Acceleration

Force

Velocity

Energy

38.

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

19/8

8/19

9/19

19/9

40. The conic is a parabola if

e = 1

e < 1

None of these

e > 1

41. The cosine of the angle between the vector a and b where a = I + 2j – k , b = -I + j – 2k is

√3/2

1/√2

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

43. A vector with magnitude one is called

Unit vector

Constant vector

Zero vector

Null vector

44. The scalar quantity in the following is

Torque

Speed

Velocity

Force

45. 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

46. An example of scalar quantity is

Power

Acceleration

Velocity

Force

47. [k – i, i – j, j – k] = ?

-1

48. The perpendicular bisector of any chord of a circle

None of these

Does not pass through the center of the circle

May or may not pass through the center of the circle

Passes through the center of the circle

49. 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/2

π/4

π/3

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

Focal axis

Conjugate axis

Major axis

Minor axis

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Vectors Chapter Online Test

ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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Danial Malik

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ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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