What are Scalar and Vector Quantities in Physics?
Quantities that can be described in terms of magnitude only are scalar quantities, while those that have both magnitude and direction are called vector quantities.
Assume that Rita is traveling from city X to Y at a speed of 30 kmph without looking into the path she is taking. On the other hand, while heading towards her office on time, she uses GoogleMaps to reach via the shortest path.
So, what difference do you find in both scenarios above? Well! The first instance talks about the scalar quantity, while the second of a vector quantity.
This page will help you understand the definition of both scalar and vector quantities along with illustrative examples.
Types of Physical Quantities
Physical quantities can be classified into two categories, which are scalars and vectors. Quantities like mass or density can be described by their numerical values and appropriate units only. These quantities are called “scalars”. However, quantities like velocity or force require the specifications of a numerical value and a direction. For example, specifying the value of velocity is not enough to understand an object’s motion.
It is necessary to mention the direction of its motion. Such quantities are referred to as vectors. The physical interpretations, algebra, and calculus are very different for the two types of quantities.
Scalar Quantity Definition
A scalar quantity only has a magnitude and it can be represented by a number only. A scalar does not have any direction. The addition of scalars follows the generic rules of the addition of numbers.
Vector Quantity Definition
A physical quantity, having both magnitude and direction, is referred to as a vector. The addition of two vectors does not follow ordinary algebra. A vector quantity is represented with an arrow over a letter or a boldface letter. Geometrically, it is represented by a line segment, having an arrow at one end. The arrow describes the direction and the length of the segment gives the magnitude.
Examples of Scalar and Vector Quantities
Some common examples of scalar quantities are mass, time, speed, volume, temperature, density, and many more.
Displacement, velocity, acceleration, momentum, force, weight, etc. quantities are represented by vectors.
Addition of vectors
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Laws of Addition of Vectors
Vector addition can be defined using any of the following laws,
1. Triangle Law:
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If two vectors are denoted by the sides of a triangle in the same order, the resultant vector is given by the third side of the triangle, taken in the opposite order.
2. Parallelogram Law:
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If two vectors are denoted by two adjacent sides of a parallelogram, the resultant vector is given by the diagonal that passes through the point of intersection of those sides.
The resultant (addition) of two vectors a and b with magnitudes a and b is given by,
c = a + b
The resultant vector c has magnitude, it makes an angle with the vector a such that,
c = tan Ө
Please note that the vector subtraction can be expressed as addition of the inverted vector to be subtracted.
Now, there are some questions that are answered to clarify the concept of both scalar and vector quantities.
Basic Concepts of Scalar and Vector Quantities - Solved QAs
1. Force is Scalar or Vector?
Force is a quantity that can change the state of motion of an object. It has both magnitude and direction. The SI unit of force is Newton (N).
2. Mass is Scalar or Vector?
Mass is a scalar quantity. It is a measure of the inertia of an object. Mass can be represented by a number only. The SI unit of mass is kg.
3. Weight is Scalar or Vector?
Weight is a vector quantity. It is given by the amount of force exerted on an object, due to a gravitational force. The weight of an object on the Earth has a direction towards the center of the Earth. SI unit of weight is Newton (N).
4. Displacement is Scalar or Vector?
Displacement of an object is given by the straight distance traversed by the object at any given time interval. It is a vector quantity and it points from initial to final position of the body within that interval of time. The SI unit of displacement is meter (m).
5. Speed is Scalar or Vector?
Speed of an object is a scalar but velocity is a vector. Velocity has a direction as that of displacement. Velocity points in the direction of motion. The SI units of both speed and velocity are m/s.
6. Acceleration is Scalar or Vector?
Acceleration of an object is caused due to the change of velocity of the object. It is a vector quantity having unit m/s2.
7. Area is Vector or Scalar?
Area is a vector quantity. It has a magnitude equal to the amount of space inside any boundary. The normal direction to that space is associated with the area. The SI unit is m2.
8. Pressure is Scalar or Vector?
Pressure is the amount of normal force per unit area. It is a scalar quantity however force is a vector. Pascal (Pa) or N/m2 is the SI unit of pressure.
9. Work is Scalar or Vector?
Work is the energy associated with a force. If a force acts on a body and the body undergoes a displacement, the amount of work done is the product of force and displacement parallel to the force. Work has the dimensions of energy, which is also a scalar. The SI unit of work is Joule (J).
Did You Know - Facts on Scalar and Vector Quantities
Below are the facts and information on scalar and vector quantities:
When an object moves along a path joining two points, the distance is measured along the trajectory whereas displacement is the shortest path joining the two points. Consequently, distance varies if the object follows different trajectories between the initial and final positions.
However, the displacement between two fixed positions is independent of the path followed by the object. Distance is a scalar, however, displacement is a vector.
Speed and velocity are closely related but different concepts. For example, the speed of an object remains constant throughout a uniform circular motion but the velocity is different at every point since the direction of velocity changes.
The weight of a body depends on its mass. Although the mass of an object remains the same, its weight can vary due to variation in the gravitational field.
FAQs on Scalar and Vector
1. What is the fundamental difference between a scalar and a vector quantity in Physics?
The fundamental difference lies in their definitions. A scalar quantity is a physical quantity that can be completely described by its magnitude (a numerical value) alone. It has no direction. In contrast, a vector quantity is a physical quantity that requires both magnitude and a specific direction for its complete description. For example, saying a car travels at 60 km/h describes its speed (scalar), but saying it travels at 60 km/h towards the east describes its velocity (vector).
2. What are some common examples of scalar and vector quantities?
Understanding the difference is easier with examples. Here are some common physical quantities categorised as scalar or vector:
- Scalar Quantities: Mass (kg), Speed (m/s), Distance (m), Time (s), Temperature (°C or K), Area (m²), Volume (m³), Energy (J), Work (J), and Pressure (Pa).
- Vector Quantities: Displacement (m), Velocity (m/s), Acceleration (m/s²), Force (N), Weight (N), Momentum (kg·m/s), and Electric Field (N/C).
3. Why is distance a scalar quantity, while displacement is a vector?
This is a classic example that highlights the core difference. Distance is the total length of the path covered by an object, regardless of its direction. It is a scalar because it only has magnitude (e.g., 'you walked 5 km'). Displacement, however, is the shortest straight-line path between the object's initial and final positions. It is a vector because it has both magnitude (how far apart the start and end points are) and direction (the direction from start to finish). An object can travel a large distance but have zero displacement if it returns to its starting point.
4. How can a physical quantity like area be considered a vector?
While the magnitude of an area is a scalar concept (the amount of space), in many physics applications, particularly in topics like flux (electric or magnetic), area is treated as a vector quantity. The magnitude of the area vector is the surface area itself. Its direction is defined as being perpendicular (or normal) to the plane of the surface. This directional property is crucial for calculating how much of a field passes through a surface.
5. If force is a vector, why is pressure, which is Force/Area, a scalar quantity?
This is a common point of confusion. While pressure is defined using force (a vector), it is a scalar quantity. Pressure is specifically the magnitude of the force acting perpendicular to a surface, per unit area. At any given point within a fluid, pressure is exerted equally in all directions. Therefore, it has no single, specific direction associated with it, only a magnitude at that point, making it a scalar.
6. How does the addition of vectors differ from adding scalars?
Adding scalars is simple arithmetic; for example, 2 kg + 3 kg = 5 kg. However, adding vectors must account for their directions. Two forces of 5N and 3N might result in 8N (if in the same direction), 2N (if in opposite directions), or any value in between, depending on the angle between them. Vectors are added using specific geometric rules like the Triangle Law of Vector Addition or the Parallelogram Law of Vector Addition, not by simply adding their magnitudes.
7. What is a zero or null vector and why is it important?
A zero vector, or null vector, is a vector with a magnitude of zero and an arbitrary or undefined direction. It is represented as Ō. Its importance arises in vector equations. For instance, if an object is in equilibrium, the vector sum of all forces acting on it is the zero vector. Similarly, the velocity vector of a stationary object is a zero vector. It acts as the additive identity in vector algebra, similar to the number 0 in scalar arithmetic.
