Practice Test 3 ( Resultant of Vector )

Vectors Practice Test 3 ( Resultant of Vector)

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1 / 27

Given A = 3i + 4j – 5k and B = 1i – 2j + 2k, the magnitude of R = A – 2B is:

A) √82

B) √100

C) √146

D) √164

2 / 27

Vectors A = 4i − 2j and B = −i + 5j act at a point. The direction of the resultant R = A + B, measured from the positive x-axis, is:

A) 30°

B) 45°

C) 60°

D) 90°

3 / 27

Three mutually perpendicular vectors of magnitudes 2, 3 and 6 units act simultaneously at a point. The magnitude of their resultant is:

A) √11

B) 7

C) √7

D) 49

4 / 27

Two vectors of magnitudes 5 units and 7 units act with an angle of 60° between them. The magnitude of their resultant is:

A) √45

B) √71

C) √109

D) √114

5 / 27

Consider vectors A = 3i + 4j and B = 2i − j. The magnitude of the resultant R = A + B is:

A) √19

B) √34

C) √29

D) √14

6 / 27

For the figure -

A) A+B=C

B) B+C=A

C) C+A=B

D) A+B+C=0

7 / 27

If the angle between the unit vectors â and b̂ is 60°, then |â − b̂| is:

A) 0

B) 1

C) 2

D) 4

8 / 27

What displacement must be added to the displacement
25 î − 6 ĵ m to give a displacement of 7.0 m pointing in the x-direction?

A) 18 î − 6 ĵ

B) 32 î − 13 ĵ

C) −18 î + 6 ĵ

D) −25 î + 13 ĵ

9 / 27

Two forces, F1 and F2 are acting on a body. One force is doubled of the other force and the resultant is equal to the greater force. Then the angle between the two forces is -

A) cos⁻¹(1/2)

B) cos⁻¹(−1/2)

C) cos⁻¹(−1/4)

D) cos⁻¹(1/4)

10 / 27

A truck travelling due north with 20m/s turns towards west and travels at the same speed. Then the change in velocity is -

A) 40 m/s north-west

B) 20√2 m/s north-west

C) 40 m/s south-west

D) 20√2 m/s south-west

11 / 27

The three vectors OA, OB and OC have the same magnitude R. Then the sum of these vectors have magnitude -

A) R

B) √2 R

C) 3R

D) ( 1 + √ 2 )R

12 / 27

A force of 6 N and another of 8 N can be applied together to produce the effect of a single force of -

A) 1 N

B) 11 N

C) 15 N

D) 20 N

13 / 27

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?

A) 2, 4, 8

B) 4, 8, 16

C) 1, 2, 1

D) 0.5, 1, 2

14 / 27

In the given figure

A) Angle between A and B is 110∘

B) Angle between C and D is 60∘

C) Angle between B and C is 110∘

D) Angle between B and C is 70∘

15 / 27

Two time-dependent vectors are defined as

A = cos t i + sin t j
B = cos (t⁄2) i + sin (t⁄2) j

At what smallest positive value of t (in radians) are A and B perpendicular?

A) π⁄2

B) π

C) 3π⁄2

D) 2π

16 / 27

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

A) 0∘

B) 90∘

C) 45∘

D) 180∘

17 / 27

Two forces are such that the sum of their magnitudes is 18N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12N. Then the magnitudes of the forces will be:

A) 4 N and 14 N

B) 5 N and 13 N

C) 6 N and 12 N

D) 7 N and 11 N

18 / 27

Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is

A) 45°

B) 120°

C) 150°

D) 60°

19 / 27

If the angle between the two forces increases, the magnitude of their resultant:

A) Decreases

B) Increases

C) Remains unchanged

D) First decreases, then increases

20 / 27

if we have two vectors P and Q and P=Q then which of the following is not correct

A) P̂ = Q̂

B) |P| = |Q|

C) P Q̂ = Q P̂

D) P + Q = P̂ + Q̂

21 / 27

If A = B + C and the magnitudes of A, B, C are 5, 4, 3 units respectively, the angle between A and C is:

A) cos⁻¹ (3⁄5)

B) cos⁻¹ (4⁄5)

C) sin⁻¹ (3⁄4)

D) π⁄2

22 / 27

Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:

A) North-East

B) North-West

C) South-West

D) South-East

23 / 27

For the given figure, which of the following is true?

A) B=A+C

B) A=B+C

C) C=A+B

D) All of these

24 / 27

If the magnitude of the sum of two vectors equals the magnitude of their difference, the angle between the vectors is:

A) 90°

B) 45°

C) 180°

D) 0°

25 / 27

There are two force vectors, one of 5 N and the other of 12 N. At what angle should the two vectors be added so that the resultant has a magnitude of 17 N, 7 N, and 13 N respectively?

A) 0°, 180° and 90°

B) 0°, 90° and 180°

C) 0°, 90° and 90°

D) 180°, 0° and 90°

26 / 27

If | v₁ + v₂ | = | v₁ − v₂ | and v₁, v₂ are non-zero vectors, then:

A) v₁ is parallel to v₂

B) v₁ = v₂

C) v₁ and v₂ are mutually perpendicular

D) | v₁ | = | v₂ |

27 / 27

Two forces A and B have a resultant R₁. If B is doubled, the new resultant R₂ is perpendicular to A. Then

A) R₁ = A

B) R₁ = B

C) R₂ = A

D) R₂ = B

Your score is

The average score is 41%

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Pos.	Name	Duration	Points
1	Javeria sher P3	37 minutes 14 seconds	8
2	Gulali P3	6 seconds	0

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