Test: Scalars and Vectors - ACT MCQ

Vector addition and subtraction give a vector as the output. Cross product also gives a vector as the output. Only Dot product gives a scalar after acting on two vectors.

Mass represents the amount of matter in a body. It does not have any direction but only mass. Hence, it is a scalar quantity.

Only operations valid for vector with scalars are multiplication and division. A vector can be multiplied or divided by a scalar. Other operations like addition and subtraction are not valid for vectors with scalars.

A scalar quantity is one which only has a magnitude. Examples of scalar quantities are mass, volume, work, energy etc.

Dot product of two vectors gives a scalar quantity as the output. Cross product gives a vector as the output. It is also known as scalar product.

The resultant vector is the vector which is obtained by the addition or subtraction of two vectors. The resultant vector can either be calculated by using the graphical method or the analytical method.

A vector quantity is one which has both magnitude and direction. Unlike scalars, it can also tell the direction in which is the entity is acting. Examples of vector quantities are force, velocity, displacement etc.

Scalar Quantity:

• It is a physical quantity which have only magnitude.
• It is totally described by a magnitude or numerical value.
• It does not have any directions.
• It is a measure of quantity.
• Multiplication of two scalar quantity would also give scalar quantity.
• Example: mass, speed, time, energy, density, volume, work, moment of inertia, etc.

Vector Quantity:

• It is a quantity which has both magnitude and direction.
• Example: a man traveling with a velocity of 20 km/hr in the north direction.
• Examples of vector quantity are Displacement, momentum, Force, velocity, etc.

Concept:

• Vector Quantity: Physical quantities that have magnitude and direction and obey triangle law are called vector quantities.
• Example: Displacement, Velocity, etc.

Additional Information 

• The velocity of a moving object is defined as the displacement of the object in the unit time interval.
• It is a vector quantity and its SI unit is meter/second.
• Acceleration of an object is defined as the rate of change of velocity of the object.
• It is a vector quantity and its SI unit is (m/s²)
• ∴ The correct answer is 20 m/s².

All physical quantities are classified into two types:

Scalar Quantity:

• A physical quantity having magnitude only is called scalar quantity. They have numerical value only and these quantities do not specify the direction
• Example: Length, Time, Speed, Mass, Density, Pressure, Temperature, Energy, Work, Power

Vector quantity:

• A physical quantity having both magnitude and direction is called vector quantities. It is represented by a straight line with an arrowhead
• Example: Displacement, Velocity, Acceleration, Force, Momentum, Weight