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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. The direction cosines of y-axis are

1, 1, 1

1, 0, 0

0, 1, 0

0, 0, 1

2. The scalar quantity in the following is

Force

Speed

Torque

Velocity

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

2/3

√3/2

√2/3

None of these

4. An example of scalar quantity is

Force

Energy

Acceleration

Velocity

5. The area enclosed by the triangle ABC whose vertices are A(1, 2, -3) B (0,0,0) and c (2, 4, 7) is

√184

√676

√845/2

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

Scalar

Variable

Vector

Constant

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

√450

√150

√50

200

8. An example of vector quantity is

Power

Work

Energy

Force

9. A vector with magnitude one is called

Null vector

Zero vector

Unit vector

Constant vector

10.

11. 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

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

19/9

9/19

19/8

8/19

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

2 – dimensional space

None of these

3 – dimensional space

One – dimensional

14. An example of vector quantity is

Power

Energy

Acceleration

Work

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

16. 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/4

π/3

π/6

π/2

17. Which is not a vector

Density

Weight

Displacement

Electrified intensity

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

60°

90°

45°

30°

19. 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

20. 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

21. 3j . k x i

22.

23. The perpendicular bisector of any chord of a circle

Does not pass through the center of the circle

None of these

Passes through the center of the circle

May or may not pass through the center of the circle

24.

25.

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26. 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

A parabola

A st. line

An ellipse

27. [k – i, i – j, j – k] = ?

-1

28. The conic is a parabola if

e < 1

None of these

e > 1

e = 1

29. The vector quantity in the following is

Temperature

Energy

Angular acceleration

Distance

30. a x b = b x c = c x a if

a = b + c

a = b = c

a + b + c = 0

Both b and c

31. The unit vector along z-axis is

None of these

k̂

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

5/√110 (– i – 3j – 10k)

6/√17 (– i + 3j – 10k)

5/√17 (– i + 3j – 10k)

5/√17 (– i – 3j – 10k)

33. A vector of magnitude zero is called

Null vector

Position vector

None of these

Free vector

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

35. The magnitude of a vector can never be

Negative

None of these

Zero

Positive

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

Conjugate axis

Focal axis

Major axis

Minor axis

37. An example of scalar quantity is

Velocity

Acceleration

Force

Power

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

√3

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

Branches

Nappes

Vertices

Directrices

40.

41. The scalar quantity in the following is

Displacement

Density

Force

Velocity

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

√74

√76

√89

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

√41

½ √17

½ √14

44. An example of scalar quantity is

Acceleration

Weight

Force

Kinetic energy

45. The vector quantity in the following is

Energy

Impulse

Temperature

Distance

46. The scalar quantity in the following is

Velocity

Force

Displacement

Time

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

None of these

48. The scalar quantity in the following is

Velocity

Pressure

Acceleration

Force

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

√2

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

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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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