Table of Contents

## Why do We need to define Vector and Scalar Quantities?

A vector quantity is a physical quantity that has both magnitude and direction. A scalar quantity is a physical quantity that has magnitude only. Magnitude is a measure of the size of a vector or scalar quantity. Direction is a measure of the orientation of a vector quantity.

## Scalar Quantity Definition

A scalar quantity is a physical quantity that has magnitude (size) but no direction. Examples of scalar quantities are mass, length, and time.

## Vector Quantity Definition

A vector quantity is a physical quantity that has both magnitude and direction. Examples of vector quantities are displacement, velocity, and force.

## Scalar Quantity Examples:

The length of a line

The weight of a rock

The temperature of a room

## Vector Quantity Examples:

speed, voltage, current, resistance, capacitance

## Addition of Vector

To add two vectors, we add the individual components of each vector.

For example, if we have the vectors:

Vector A = (3, 2, 1)

Vector B = (4, 5, 6)

We would add the components like so:

Vector A + Vector B = (7, 7, 7)

## Subtraction of Vector

To subtract one vector from another, simply subtract the corresponding components of the vectors.

For example, to subtract the vector A = (3, 4, 5) from the vector B = (1, 2, 3), we would compute:

A – B = (3, 4, 5) – (1, 2, 3) = (2, 2, 2)

## Difference between Scalar and Vector Quantity

There is a fundamental difference between scalar and vector quantities. Scalar quantities are those that have magnitude but no direction, whereas vector quantities have both magnitude and direction. For example, displacement is a vector quantity, whereas mass is a scalar quantity.

## Notation

The following notation is used in this paper.

n denotes the number of input neurons.

x 1 , x 2 , …, x n denote the input values.

, x , …, x denote the input values. y denotes the output value.

h(x) denotes a function.

W 1 , W 2 , …, W n denote the weights of the n input neurons.

## Few interesting Facts About Scalars and Vectors

A scalar is a single value, while a vector is a set of values.

A vector has both magnitude and direction.

A scalar has magnitude only.

A vector can be represented as an arrow, with the magnitude represented by the length of the arrow and the direction represented by the direction the arrow is pointing.

A vector can be added or subtracted by combining the magnitudes and adding or subtracting the directions.

A vector can be multiplied by a scalar, which will multiply the magnitude of the vector by the scalar value.

A vector can be divided by a scalar, which will divide the magnitude of the vector by the scalar value.