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MCQ on Fundamental Vectors

A vector is a quantity which has both magnitude and the direction but not location in mathematics. Velocity and acceleration are two examples of such numbers. Vector analysis was invented separately by Josiah Willard Gibbs and Oliver Heaviside (of the United States and the United Kingdom, respectively) late in the nineteenth century to explain the new principles of electromagnetic discovered by Scottish scientist James Clerk Maxwell. Since then, vectors have been indispensable in physics, mechanics, electrical engineering, and other fields for quantitatively describing forces.

Vectors can be represented as directed line segments with lengths equal to their magnitudes. Because just the magnitude and direction of a vector matter, any directed segment may be substituted by one that is the same length and direction but starts at a different location, such as the coordinate system’s origin.

MCQs

  1. For a vector quantity, which of the following is true?
  1. It just has the magnitude
  2. It has only the direction
  3. It has both the magnitude as well as the direction
  4. None of the mentioned

Answer: Correct option will be: (c) It has both the magnitude as well as the direction.

Reason: A vector quantity is a quantity that has both magnitude and direction. A scalar quantity is a quantity that has simply magnitude and no direction.

2. Which of the mentioned is the proper sign for a vector A?

  1. A
  2. A
  3. A
  4. A⇀

Answer: Correct option will be: (c) A.

3. To express the magnitude of vector A Which of the below is used? 

  1. A
  2. A
  3. A
  4. A⇀

Answer: Correct option will be: (b) A.

4. What will be the vertical component of a force of 5 N acting on a particle in a 60° angle?

  1. 3N
  2. 2.5N
  3. 10N
  4. 4N

Answer: Correct option will be: (b) 2.5N.

Calculation: The vertical component of the force will be: Fv=Fcos

Here Fy is the vertical component of force, F is the magnitude of the force and is the angle of the application of force.

Fy=5cos 60

     =5×0.5

     =2.5N

5. What is the smallest number of distinct magnitude coplanar vectors that can be joined to yield a consequent of zero?

  1. 1
  2. 2
  3. 3
  4. 4

Answer: Correct option will be: (c) 3.

6. What will be the y-component of the same applied force if the x-component of a force of 50N is 30N?

  1. 20N
  2. 25N
  3. 40N
  4. 45N

Answer: Correct option will be: (c) 40N.

Calculation: to solve this we will use the formula: F=Fx2+Fy2

🡺50=302+Fy2

🡺Fy2=2500-900

🡺Fy2=1600

🡺Fy=40N

7. Two forces of 4 N and 3 N act on a particle at the same time. The particle’s net force is equal to:

  1. 1N
  2. 7N
  3. 5N
  4. Between 1N and 7N

Answer: Correct option will be: (d) Between 1N and 7N.

Reason: Depending on the angle between the forces, the resultant force will be in between 1N and 7N.

1N will be the minimum resultant force when the forces act in opposite directions whereas 7N will be the maximum resultant force when the forces act in the same direction.

8. What will be the projection on the y axis of the vector 3i+4k:

  1. 7
  2. 1
  3. 4
  4. 0

Answer: Correct option will be: (d) 0.

9. In a rectangular-coordinate system, a particle’s position is (3, 2, 5). Then it will have a position vector of

  1. 3i+5j+2k
  2. 3i+2j+5k
  3. 5i+3j+2k
  4. None of the mentioned

Answer: Correct option will be: (b) 3i+2j+5k.

10. The displacement vector of the particle when it has travelled from point P(2,3,5) to Q(3,4,5) will be:

  1. i+j+10k
  2. i+j+5k
  3. i+j
  4. 2i+4j+6k

Answer: Correct option will be: (c)i+j.

Calculation: The displacement vector will be calculated as: D=Q-P

🡺D=3i+4j+5k–2i+3j+5k

🡺D=i+j

11. What is the other way of mentioning the vector 12i+12j

  1. Unit vector
  2. Null vector
  3. Vector of magnitude 2
  4. Scalar

Answer: Correct option will be: (a) Unit vector.

Calculation: A=12i+12j

🡺A=122+122

🡺A=12+12

            =1=1

12. The angle formed by the vector (1,1) with respect to the x-axis is:

  1. 90o
  2. 45o
  3. 22.5o
  4. 30o

Answer: Correct option will be: (b) 45o

Calculation: the angle formed by the vector with the x axis will be:  θ = tan -1 (y/x)

🡺θ = tan-1(1/1)= 450.

13. Find the value of c for which the vector 0.4i+0.7j+c k is a unit vector.

  1. 0.35
  2. 1.44
  3. 0.22
  4. 0.67

Answer: Correct option will be: (a) 0.35.

Calculation: A=0.4i+0.7j+c k

If A=1 then

1=0.42+0.72+c2
🡺1-0.16-0.49=c2

🡺c=0.35

14. What will be the resultant of A×0

  1. Zero vector
  2. Unit vector
  3. A
  4. None of the mentioned

Answer: Correct option will be: (a) Zero vector.

15. Which of the given quantities is a vector quantity?

  1. Electrostatic energy
  2. Electric field Intensity
  3. Electrostatic potential
  4. Electric current

Answer: Correct option will be: (b)Electric field intensity.

16. If the initial and terminal points of a vector are coincident then the vector is called as:

  1. Zero vector
  2. Free vector
  3. Unit vector
  4. Equal vector

Answer: Correct option will be: (a) Zero vector.

Reason: A null vector is defined as a vector with magnitude equal to zero. The letter O is commonly used to represent it. A null vector is commonly used to represent a point.

17.In a hall with dimensions of 10m×12m×14m, a fly takes off from one corner and lands in the diametrically opposite corner. What is the size of the bird’s flight?

  1. 17m
  2. 21m
  3. 26m
  4. 36m

Answer: Correct option will be: (b)21m.

18.Any vector in any direction can be substituted by two or three vectors that are:

  1. Perpendicular to one another and have the initial vector as their consequent 
  2. Parallel to one another and have the initial vector as their resultant 
  3. Arbitrary vectors with initial vectors as their resultant 
  4. The resolution of the vector is impossible.

Answer: The correct option will be: (c) Arbitrary vectors with initial vectors as their resultant.