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Scalar and Vector Quantity

Physics deals with the measurement of various quantities, and these quantities have unique features of their own. To make studying these quantities easy and form a systemic model, we use several categories. One such model includes the use of scalar and vector quantities.
Every quantity in the physical world is categorised either under scalar or vector quantities. These categories help determine the behaviour of the quantities and the rules that govern their arithmetic operations.

What is a scalar quantity?

A scalar quantity only has a magnitude and lacks any direction. The quantities follow the laws of regular arithmetic operation.
Distance, Speed, and energy are some of the scalar quantities.

What is a vector quantity?

A vector quantity is something that has direction along with a magnitude. The vector quantities follow the laws of vector addition.
Displacement, Velocity, and Work some of the vector quantities.

How to denote a vector quantity?

In physics and mathematics, we denote a vector quantity by an arrow above the variable defining it. For example, we write the velocity vector with the '→' symbol over the letter v. The value contains the magnitude of velocity followed by the unit vector in the direction of the velocity.

What is vector addition?

One cannot add the vector quantities or subtract using the arithmetic rules used with the scalar quantities. Therefore, the rules that govern vector operations are very different, and it involves a vector quadrilateral. The rules for making a vector quadrilateral are as follows:

  • Vector is drawn by taking a scale and converting the length accordingly. The direction is the same as the vector.
  • We draw the next vector by drawing starting at the arrow end of the previous vector.
  • We can obtain the resultant vector by joining the first vector's tail end to the last vector's arrow end. The length gives the magnitude, and the direction of the arrow-end gives the direction.
  • The vector addition is commutative i.e. vector A + vector B = vector B + vector A.
  • The vector components behave as they are independent of each other.

Difference between Scalar and Vector Quantities

Scalar

Vector

These quantities have a magnitude and no direction

These quantities have a direction and a magnitude

A value (magnitude) followed by the unit represents these quantities. 

A magnitude and a unit vector in the direction along with the unit represent the vector quantities. 

The variable/symbol has an arrow sign to show the direction. 

The symbol has no extra entity. 


Laws Related to Vector Addition

Two prominent laws deal with the concept of vector addition:

  • Triangle Law: The law states that if we represent two vectors as the two sides of a triangle (in both magnitude and direction), then the third side of the triangle gives the resultant of the two vectors.
  • Parallelogram Law: The parallelogram law of vectors suggests that if the two sides of the parallelogram represent the two vectors, then the resultant of the vector is the diagonal of the parallelogram originating from the common point.

Properties of Vector Addition

  • Vector addition is associative. The result of vectors (A+B)+C = A+ (B+C)
  • Vector addition is commutative. The result of A+B is the same as the result of B+A.

Frequently Asked Questions about Scalar and Vector Quantities

Ques: What is the key difference between a scalar quantity and a vector quantity?
The key difference is direction. Scalar Quantity has magnitude only and no direction. A vector quantity, on the other hand, has a magnitude and direction.

Ques: What are the points of similarity in scalar and vector quantities?
The point of similarity in vector and scalar quantities is that they are both measurable quantities and have magnitude followed by well-defined units of measurement.

Ques: Explain the difference between the scalar quantities and vector quantities using the example of distance and displacement.
Both distance and displacement are measurements of length. Distance is the total length covered by a body, whereas displacement is the shortest distance between two endpoints. Where distance is just the length, displacement is along a certain direction, giving the shortest length between the starting and the endpoint. Thus, distance only has a value, but displacement has a direction along with a value.

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