Quiz: Chapter 1 - Vectors and Equilibrium

1 Which of the given quantity is a vector?

Pressure Kinetic energy Momentum Volume

2 Vectors have:

Numerical properties Directional properties Both numerical and directional properties None of these

3 A null vector has:

Zero magnitude and a specific direction A finite magnitude and no specific direction A finite magnitude and a specific direction Zero magnitude and no specific direction

4 Pick out the only vector quantity:

Pressure Impulse Gravitational potential Coefficient of friction

5 A unit vector is obtained by dividing the vector with:

Its magnitude and direction Its direction Scalar quantity Its magnitude

6 A force of 5N is acting along y-axis. Its component along x-axis is:

5N Zero 10N 2.5N

7 At what angle do components of a vector have the same magnitude?

0° 30° 45° 90°

8 If 𝑨⃗⃗ = 2𝒊̂− 𝒋̂+ 3𝒌̂, then magnitude of A is:

4 14 √14 None of these

9 A physical quantity with magnitude and direction but not obeying parallelogram law is:

Must be a vector May be both scalar and vector May be a vector Scalar

10 What is the minimum number of vectors giving zero resultant?

2 3 4 Infinite

11 If vector A makes angle θ with x-axis, its x-component is:

A sinθ A tanθ A cosθ A sin x

12 Which is NOT a vector?

Distance Position Magnitude of a vector Resultant of a vector

13 Unit vector specifies:

Direction of a vector Position of a vector Magnitude of a vector Resultant of a vector

14 A vector with zero magnitude is called:

Null vector Equal vector Unit vector Resultant vector

15 When a vector is multiplied by a negative number, its direction:

Remains same Changes by 180° Does not change None

16 The single vector equivalent to multiple vectors combined is called:

Unit vector Position vector Resultant vector None

17 A 10N vector at 45° has rectangular components with angle:

45° 90° 135° 0°

18 If two unit vectors are at 90°, their resultant magnitude is:

2 √2 √(1/2) 0

19 The sum of a vector and its negative is:

Unit vector Null vector Zero Position vector

20 Two perpendicular lines are called:

Vector lines Scalar lines Coordinate axes All

21 In head-to-tail rule, the resultant is directed from:

Last vector to 1st vector First to last vector Both A & B Arbitrary

22 Vector subtraction is:

Commutative Non-commutative Sometimes commutative None

23 If 𝒂⃗⃗ and 𝒃⃗⃗ are antiparallel, their resultant is:

𝒂 + 𝒃 𝒂 − 𝒃 2𝒂 2𝒃

24 A component of a vector is its effective value in a given:

Space Plane Direction Axis

25 Rectangular components of a vector are:

Parallel Antiparallel Perpendicular All

26 To add vectors, we use:

Head-to-tail rule Right-hand rule Hit and trial None

27 Resultant of 3N and 4N at right angles is:

5N 6N 2N 7N

28 If 𝑨⃗⃗ =4𝒊̂, 𝑩⃗⃗ =−4𝒋̂, angle of 𝑨⃗⃗ + 𝑩⃗⃗ with x-axis is:

45° 135° 225° 315°

29 Which is perpendicular to 4𝒊̂− 3𝒋̂?

4𝒊̂+ 3𝒋̂ 6𝒊̂ 7𝒌̂ 3𝒊̂− 4𝒋̂

30 If |𝑨⃗⃗ × 𝑩⃗⃗ | = 0, the angle between A and B is:

0° 90° 180° None

31 Angle between 𝑨⃗⃗ =4𝒊̂+3𝒋̂−2𝒌̂ and 𝑩⃗⃗ =8𝒊̂+6𝒋̂−4𝒌̂ is:

45° 60° 0° 90°

32 𝒋̂·(𝒊̂×𝒌̂) =

1 0 -1 0⃗

33 Work done by 𝑭⃗⃗ =2𝒊̂+3𝒋̂ over 𝒅⃗⃗ =4𝒊̂−2𝒋̂ is:

2J 6J 4J 8J

34 Scalar product obeys:

Commutative Distributive Associative All

35 If A is along x-axis and A × B = 0, B could be:

4𝒋̂ -4𝒋̂ −(𝒊̂+𝒋̂) 𝒋̂+𝒌̂

36 If A·B = 0, angle θ is:

30° 60° 45° 90°

37 Cross product î × î =

1 -1 î 0

38 If 𝑨⃗⃗ × 𝑩⃗⃗ = 𝑩⃗⃗ × 𝑨⃗⃗ , angle θ is:

π π/3 π/2 π/4

39 If 𝑨⃗⃗ ·𝑩⃗⃗ = |𝑨⃗⃗ ×𝑩⃗⃗ |, angle θ is:

0 π/4 π/2 π

40 A vector perpendicular to 4𝒊̂−3𝒋̂ is:

−4𝒊̂+3𝒋̂ −3𝒊̂−4𝒋̂ 7𝒌̂ Both B & C

41 Cross product is negative when vectors are:

Parallel Antiparallel Perpendicular None

42 Dot product î·î =

0 1 -1 2

43 Distance vector from A(2,3,4) to B(−5,6,7) is:

7𝒊̂+9𝒋̂+11𝒌̂ −7𝒊̂−9𝒋̂−11𝒌̂ −7𝒊̂+3𝒋̂+3𝒌̂ −3𝒊̂−3𝒋̂−3𝒌̂

44 Area of parallelogram formed by A and B is:

AB AB cosθ AB sinθ AB tanθ

45 Angle between 𝑨⃗⃗ =𝒋̂+𝒌̂ and 𝑩⃗⃗ =−𝒋̂−𝒌̂ is:

90° 180° 270° 360°

46 If A points up and B points down, A × B is:

West East Zero Down

47 Dot product of two perpendicular vectors of magnitude A is:

A 2A 0 A²

48 Self-cross product of A is:

√A 1/A A² 0

49 The magnitude of 𝑨⃗⃗ × 𝑩⃗⃗ represents:

Area of triangle Area of parallelogram Volume of parallelepiped None

50 If |𝑨⃗⃗ + 𝑩⃗⃗ | = |𝑨⃗⃗ − 𝑩⃗⃗ |, angle between A and B is:

0° 45° 90° 180°

51 The projection of 𝑨⃗⃗ on 𝑩⃗⃗ is given by:

(𝑨⃗⃗ ·𝑩⃗⃗ )/|𝑩⃗⃗ | |𝑨⃗⃗ ×𝑩⃗⃗ |/|𝑩⃗⃗ | |𝑨⃗⃗ +𝑩⃗⃗ | None

52 If 𝑨⃗⃗ = 3𝒊̂ + 4𝒋̂ and 𝑩⃗⃗ = 𝒊̂ − 𝒋̂, then 𝑨⃗⃗ ·𝑩⃗⃗ =

7 -1 5 1

53 The direction of 𝑨⃗⃗ × 𝑩⃗⃗ is determined by:

Left-hand rule Right-hand rule Parallelogram law None

54 If 𝑨⃗⃗ and 𝑩⃗⃗ are parallel, then 𝑨⃗⃗ × 𝑩⃗⃗ =

|𝑨⃗⃗ ||𝑩⃗⃗ | 1 0 None

55 The scalar triple product 𝑨⃗⃗ ·(𝑩⃗⃗ ×𝑪⃗⃗ ) represents:

Area Volume Perimeter Diagonal

56 If 𝑨⃗⃗ ·𝑩⃗⃗ = |𝑨⃗⃗ ||𝑩⃗⃗ |, the angle between A and B is:

0° 45° 90° 180°

57 The vector 𝑨⃗⃗ × (𝑩⃗⃗ × 𝑪⃗⃗ ) is:

Perpendicular to A Parallel to A Lies in the plane of B and C None

58 If |𝑨⃗⃗ × 𝑩⃗⃗ | = 𝑨⃗⃗ ·𝑩⃗⃗ , the angle θ is:

30° 45° 60° 90°

59 The magnitude of the resultant of two vectors of magnitudes 3 and 4 at 60° is:

5 6 7 √37

60 If 𝑨⃗⃗ + 𝑩⃗⃗ = 𝑨⃗⃗ − 𝑩⃗⃗ , then:

A = B B is null vector A is null vector A ⊥ B

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Chapter 1: Vectors and Equilibrium