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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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Page 1 of 2

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

√2

2. The scalar quantity in the following is

Displacement

Velocity

Force

Density

3. An example of vector quantity is

Power

Work

Force

Energy

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

8/19

9/19

19/8

19/9

6. The magnitude of a vector can never be

Zero

Negative

None of these

Positive

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

√3

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

A circle

An ellipse

A st. line

A parabola

10. 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

11.

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

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

Focal axis

Conjugate axis

Major axis

Minor axis

14. [k – i, i – j, j – k] = ?

-1

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

√290

√279

√297

16. a x b = b x c = c x a if

Both b and c

a = b + c

a = b = c

a + b + c = 0

17.

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

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

√150

√50

200

√450

20. An example of scalar quantity is

Force

Kinetic energy

Acceleration

Weight

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

None of these

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

Directrices

Nappes

Branches

Vertices

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

√74

√89

√76

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

30°

60°

90°

45°

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

Variable

Vector

Scalar

Constant

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26. The unit vector along z-axis is

k̂

None of these

27. A vector of magnitude zero is called

None of these

Free vector

Null vector

Position vector

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

29. Which is not a vector

Density

Weight

Displacement

Electrified intensity

30. The perpendicular bisector of any chord of a circle

None of these

May or may not pass through the center of the circle

Passes through the center of the circle

Does not pass through the center of the circle

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

√41

½ √17

½ √14

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

2 – dimensional space

One – dimensional

3 – dimensional space

None of these

33. 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

34. 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

35. The scalar quantity in the following is

Displacement

Force

Velocity

Time

36. An example of scalar quantity is

Velocity

Power

Force

Acceleration

37. The vector quantity in the following is

Distance

Energy

Impulse

Temperature

38.

39. 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

40. An example of scalar quantity is

Force

Acceleration

Velocity

Energy

41. 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/√110 (– i – 3j – 10k)

5/√17 (– i – 3j – 10k)

42. 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/3

π/4

π/2

43. The vector quantity in the following is

Distance

Energy

Angular acceleration

Temperature

44. The scalar quantity in the following is

Force

Acceleration

Pressure

Velocity

45. The direction cosines of y-axis are

1, 0, 0

1, 1, 1

0, 1, 0

0, 0, 1

46. A vector with magnitude one is called

Unit vector

Constant vector

Zero vector

Null vector

47. The conic is a parabola if

None of these

e < 1

e > 1

e = 1

48. The scalar quantity in the following is

Velocity

Speed

Torque

Force

49. 3j . k x i

50. An example of vector quantity is

Acceleration

Work

Power

Energy

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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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ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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