Equality of Vectors

Two vectors are considered to be equal when they have the same magnitude and same direction. The figure below shows two vectors that are equal, notice that these vectors are parallel to each other and have the same length. The second part of the figure shows two unequal vectors, which even though have the same magnitude, are not equal because they have different directions. 

Scalar and Vector

Scalar and Vector Quantities are used to describe the motion of an object. Scalar Quantities are defined as physical quantities that have magnitude or size only. For example, distance, speed, mass, density, etc.

However, vector quantities are those physical quantities that have both magnitude and direction like displacement, velocity, acceleration, force, etc. It should be noted that when a vector quantity changes its magnitude and direction also change similarly, when a scalar quantity changes, only its magnitude changes.

Table of Content

  • Scalar Quantities Definition
  • Vector Quantities 
  • Vector Notation
  • Scalar and Vector Quantity
  • Equality of Vectors
  • Multiplication of Vectors with Scalar
  • Addition of Vectors
  • Triangle Law of Vector Addition
  • Parallelogram Law of Vector Addition
  • Examples on Scalar and Vector

Similar Reads

Scalar Quantities Definition

A scalar quantity is a physical quantity that has only magnitude and no direction....

Vector Quantities

A vector quantity is a physical quantity that has both magnitude and direction....

Vector Notation

Vector notation is a way or notation used to represent a quantity that is a vector, through an arrow (⇢) above its symbol, as shown below:...

Scalar and Vector Quantity

The differences between Scalar and Vector Quantities are shown in the table added below,...

Equality of Vectors

Two vectors are considered to be equal when they have the same magnitude and same direction. The figure below shows two vectors that are equal, notice that these vectors are parallel to each other and have the same length. The second part of the figure shows two unequal vectors, which even though have the same magnitude, are not equal because they have different directions....

Multiplication of Vectors with Scalar

Multiplying a vector a with a constant scalar k gives a vector whose direction is the same but the magnitude is changed by a factor of k. The figure shows the vector after and before it is multiplied by the constant k. In mathematical terms, this can be rewritten as,...

Addition of Vectors

Vectors cannot be added by usual algebraic rules. While adding two vectors, the magnitude and the direction of the vectors must be taken into account....

Triangle Law of Vector Addition

Consider the vectors given in the figure above. The line PQ represents the vector “p”, and QR represents the vector “q”. The line QR represents the resultant vector. The direction of AC is from A to C....

Parallelogram Law of Vector Addition

This law is just another way of understanding vector addition. This law states that if two vectors acting on the same point are represented by the sides of the parallelogram, then the resultant vector of these vectors is represented by the diagonals of the parallelograms....

Examples on Scalar and Vector

Example 1: Find the magnitude of v = i + 4j....

Scalars and Vectors-FAQs

What do you mean by Scalars and Vectors, in physics?...

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