# Vectors, Objectives, Scalars and Vectors, Vectors as a Directed Line Segment

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## Objectives:

After studying this lesson, you will be able to:

Explain the need of mentioning direction;

Define a scalar and a vector;

Distinguish between scalar and vector;

Represent vectors as directed line segment;

Determine the magnitude and direction of a vector;

Classify different types of vectors-null and unit vectors;

Define equality of two vectors;

Define the position vector of a point;

Add and subtract vectors;

Multiply a given vector by a scalar;

State and use the properties of various operations on vectors;

Comprehend the three dimensional space;

Resolve a vector along two or three mutually perpendicular axes;

Derive and use section formula; and

Define scalar (dot) and vector (cross) product of two vectors.

Define and understand direction cosines and direction ratios of a vector.

Define triple product of vectors.

Understand scalar triple product of vectors and apply it to find volume of a rectangular parallelepiped.

Understand coplanarity of four points.

## Scalars and Vectors:

A physical quantity which can be represented by a number only is known as a scalar i.e., quantities which have only magnitude.

Time, mass, length, speed, temperature, volume, quantity of heat, work done etc. are all scalars.

The physical quantities which have magnitude as well as direction are known as vectors.

Displacement, velocity, acceleration, force, weight etc. are all examples of vectors.

## Vectors as a Directed Line Segment:

You may recall that a line segment is a portion of a given line with two end points. Take any line (called a support).

The portion of with end points and is called a line segment.

The line segment along with direction from to is written as and is called a directed line segment.

and are respectively called the initial point and terminal point of the vector .

The length is called the magnitude or modulus of and is denoted by.

In other words the length.

Scalars are usually represented by etc. whereas vectors are usually denoted by etc. Magnitude of a vector i.e., is usually denoted by ‘’.