# 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;

• 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. Vectors as a Directed Line SegmentVectors as a Directed 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 ‘’.

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