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# Basic Concepts of Vectors | Difference between Vector and Scalar

June 20, 2022

Vector refers to an object that has both a direction and a magnitude. In this article, we will discuss the Basic Concepts of Vectors.

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## Basic Concepts of Vectors

Quantities that can be measured and have physical significance are called physical quantities.

There are two types of physical quantities.

• Scalar quantities  or nondirectional quantities
• Vector quantities or directional quantities

## Representation of a vector

There are two methods for vector representation

• Symbolic representation
• Graphical representation

### Symbolic representation

There are many types of symbolic representation.

### In books

• A vector represents by boldface letters like A, d,r, etc
• The magnitude of the vector is represented by light face letters such as A,d,r, etc

### Handwritten

A vector is also represented by a letter with an arrow drawn above or below it .such as

### Graphical representation of Vector

• Graphically a vector is represented by a single straight line with an arrowhead at one end
• The length of the line, according to the proper scale, gives the magnitude
• Arrow describes the direction of the vector

If 1cm =1N

Then 10N graphically represent as

## Rectangular coordinate system

The system of coordinate axes is called a cartesian or rectangular coordinate system.

### Coordinate axes

Two lines drawn mutually perpendicular to each other are known as coordinate axes.

### Origin

The point of intersection of reference or coordinate axes is called the origin. It is denoted by O

## The rectangular coordinate system in two dimension

The line in the horizontal direction is called X-axis. The X-axis is taken positive along (rightward)OX while negative along(leftward)OXâ€™.

The line in the vertical direction is called Y-axis. Y-axis is taken positive along (upward)OY while negative along(downward)OYâ€™.

### Direction of vector

The direction of a vector in a plane is obtained by the angle that a vector makes with a positive X-axis in the anti-clockwise direction.

Point P has coordinates (a,b) and vector A makes an angel Î¸ with a positive X-axis. We can reach at point P by moving the â€˜a’ unit along the positive X-axis and the â€˜bâ€™ unit along the positive Y-axis from the origin.

## The rectangular coordinate system in three dimensions (space)

There are 3 coordinates in space

The direction of a vector in space is specified by three

angles, Î±, Î², and Î³ which a vector makes with X, Y and

Z-axis respectively.

Point P of vector A has three coordinates (a,b,c). In space, we can reach point P by moving unit â€˜aâ€™ along the positive X-axis â€˜bâ€™ unit along the positive Y-axis, and â€˜câ€™ along the positive Z-axis from the origin.

### What is a vector in physics?

A vector is a physical quantity that has both magnitude and direction. It can also be thought of as the mathematical or geometrical representation of such a quantity. Examples of vectors in nature include velocity, momentum, force, electromagnetic fields, and weight.

### Is force a vector?

Yes, a force has both magnitude and direction, so Force is a vector quantity. It is denoted by F and its unit is Newton.

### Is gravity a vector quantity?

Yes, the gravitational field strength is a vector quantity as it consists of force. As force is a vector quantity, it naturally makes it a vector quantity. A scalar quantity will only have magnitude, i.e. a number.

### Is impulse a vector quantity?

An impulse is a vector quantity, so a negative impulse indicates that the net force is directed in the negative direction. Likewise, a positive impulse signifies that the net force is directed in the positive direction.

### How can we find the direction of a vector?

The direction of a vector in a plane is obtained by the angle that a vector makes with a positive X-axis in the anti-clockwise direction.

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