Vectors MCQ Quiz - Objective Question with Answer for Vectors - Download Free PDF

option(3)

CONCEPT:

• Vector quantities are those physical quantities that have both magnitude and direction and obey the vector law of addition are called vector quantities or vectors.
  • Example Displacement, Velocity, Force, Momentum, etc
• If a vector is multiplied by a real number then both the magnitude and direction of the vector remain change.

EXPLANATION:

• Multiplication of a vector by a real number
• If a vector  is multiplied by the real number λ = 2 then we get another vector  such that  = 2, as shown in the figure you can see that the magnitude of  is twice the magnitude of  while the direction of  is same as that of 

Additional Information

• If a vector is multiplied by real number λ = -2, then the new vector is such that = -2 . As shown in the above figure the magnitude of is again twice the magnitude of but the direction is opposite to that of 
• Hence we understood that If a vector is multiplied by a real number then both the magnitude as well as the direction of the vector remain change.

Given:

Calculation:

The unit vector in the direction of the vector,  

⇒ 

⇒ 

⇒ 

⇒ 

Magnitude or  = 

⇒  =  = 

Unit vector in the direction of 

⇒ 

⇒ 

∴ The required vector is 

Calculation: 

= 

= 

∴ the torque about the origin is 

CONCEPT:

• All measurable quantities are divided into two broad categories:

EXPLANATION:

• Energy is quantity has only magnitude. It does not require any direction. So it is a scaler, not vector quantity.
• The weight of a body denotes gravitational force. And force requires magnitude and direction (in which direction it is acting) both to describe.
  • So weight is a vector.
• Similarily momentum requires magnitude and direction (in which direction it is acting) both to describe.
  • So momentum is a vector.
• In chemistry, you will study that the Nuclear spin of an electron has two directions clockwise and anti-clockwise. So it will also be a vector. 

CONCEPT:

• Speed: The rate of change of distance is called speed.
  • It is a scalar quantity.
• Velocity: The rate of change of displacement is called velocity. 
  • It is a vector quantity.
• Scalar quantities: The physical quantities which have only magnitude and no direction are called scalar quantities or scalars.
  • Examples: Mass, volume, density, time, temperature, electric current, Luminious intensity, speed, etc.
• Vector quantities: The physical quantities which have both magnitude and direction and obey the laws of vector addition are called vector quantities or vectors.
  • Examples Displacement, velocity, acceleration, force, momentum, Impulse, etc.

EXPLANATION:

1. Time is a scalar quantity.
2. Volume is a scalar quantity.
3. Speed is a scalar quantity.
4. Velocity is a vector quantity. So option 4 is correct.

CONCEPT:

• All measurable quantities are divided into two broad categories:

EXPLANATION:

• From the above table, it is clear that force, velocity, and acceleration are vector quantity because they have both magnitude as well as direction. Therefore option 1, 2, and 3 is incorrect.
• Pressure is defined as force per unit area. It is a scalar quantity because it has only magnitude and it is independent on the size of the area chosen. Therefore option 4 is correct.

The correct answer is 40N

CONCEPT:​

• Resolution of vectors into components: We have a vector (F) where the magnitude of the vector is F and the angle with horizontal is θ.

The vector has two components: 1. Vertical component and 2. Horizontal component

Vertical component (F_y) = F Sinθ

Horizontal component (F_x) = F Cosθ 

Here 

CALCULATION:

Here F₁ and F₂ are along X- and Y- direction.

Let the applied force F = 50

And the x-component of the applied force F_x = 30

The y-component of the applied force F_y = ?

We know that the vector sum of the force

Now squaring both sides

2500 = 900 + F²

So option 3 is correct.

CONCEPT:

• Speed: The rate of change in distance is called speed. 
  • It is a scalar quantity. It is the magnitude of velocity that can never be negative.
• Mass: The quantity of matter in any object is called the mass of that object.
  • It can never be negative. It is a scalar quantity.
• Velocity: The rate of change in displacement is called velocity.
  • It is a vector quantity that can be negative, positive, or zero.
• Distance: The total path length between two points is called distance.
  • It is a scalar quantity and can never be negative.

EXPLANATION:

• As discussed above, velocity is a vector quantity that can be negative. So option 3 is correct.

Additional Information

• Scalar quantities: The physical quantities which have only magnitude and no direction are called scalar quantities or scalars.
  • A scalar quantity can be specified by a single number, along with the proper unit.
  • Examples: Mass, volume, density, time, temperature, electric current, Luminious intensity, etc.
• Vector quantities: The physical quantities which have both magnitude and direction and obey the laws of vector addition are called vector quantities or vectors.
  • A vector quantity is specified by a number with a unit and its direction.
  • Examples Displacement, velocity, force, momentum, etc

CONCEPT:

• All measurable quantities are divided into two broad categories:

EXPLANATION:

• From the above, it is clear that mass, length, and speed are scalar quantity because they have the only magnitude. Therefore option 1, 2, and 3 is incorrect.

• Impulse is a vector quantity because the force is a vector quantity. So option 4 is an example of a vector quantity.

CONCEPT:

• Acceleration (a): The rate of change of the velocity of an object is called acceleration.
  • It is a vector quantity.
• Scalar quantities: The physical quantities which have only magnitude and no direction are called scalar quantities or scalars.
  • Examples: Mass, volume, density, time, temperature, electric current, Luminious intensity, etc.
• Vector quantities: The physical quantities which have both magnitude and direction and obey the laws of vector addition are called vector quantities or vectors.
  • Examples Displacement, velocity, acceleration, force, momentum, Impulse, etc.

EXPLANATION:

• Acceleration is a vector quantity. So option 1 is correct.

CONCEPT:

• Force: The interaction which after applying on a body changes or try to change the state of rest or state of motion is called force.
  • It is a vector quantity.
• Temperature: The measurement of hotness is called temperature.
  • It is a scalar quantity.
• Scalar quantities: The physical quantities which have only magnitude and no direction are called scalar quantities or scalars.
  • Examples: Mass, volume, density, time, temperature, electric current, Luminious intensity, etc.
• Vector quantities: The physical quantities which have both magnitude and direction and obey the laws of vector addition are called vector quantities or vectors.
  • Examples Displacement, velocity, acceleration, force, momentum, Impulse, etc.

EXPLANATION:

1. Displacement is a vector quantity as it is directed from the initial point to the final point. 
2. Current: The rate of flow of electric charge is called current.
3. Temperature is NOT a vector quantity. It is a scalar quantity. So option 2 is correct.
4. Drag is also a type of force and it is a vector quantity.
5. Force is a vector quantity.

CONCEPT:

The dot product of vector:

• The dot product is the sum of the products of the corresponding entries of the two sequences of numbers.
• Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them.

Where  are the magnitudes of two vectors A1 and A2

EXPLANATION:

• The angle between two vectors  and  given by

• Therefore option 4 is correct.

Concept:

Physical quantities are of two types:

Explanation:

Electric Field Intensity (E):

• The space around an electric charge in which its influence can be felt is known as the electric field.
• The electric field intensity at a point is the force experienced by a unit positive charge placed at that point.
• Electric Field Intensity is a vector quantity. It is denoted by ‘E’.
• Electric Field = F/q.
• Unit of E is NC-1 or Vm-1

Electrostatic energy and electrostatic potential are scalar quantities because it only requires magnitude and not the direction.

Mistake Points

• In the case of electric current, when two currents meet at a junction, the resultant current of these will be an algebraic sum and not the vector sum.
• Therefore, an electric current is a scalar quantity although it possesses magnitude and direction.