Math 301[Calculus-III]

Text Book: Thomas Calculus Early TranscendentalEdition: 12Publisher: Pearson

VECTORS Exercise 12.2

Page 690

Module - I

In this lesson you will learn:

Three-Dimensional Coordinate System What is a Vector Component of a Vector Magnitude of a vector Addition of Vectors Scalar Multiplication Negative of a Vector Unit Vector Standard unit vectors

What is a Vector?

• A quantity that has both– Size– Direction

• Examples– Wind– Boat or aircraft travel– Forces

• Geometrically– A directed line segment

6

Initial point

Terminal point

Vector: 

Component of a Vector

If , are the points then position vector equal to is

 

 

Magnitude of a VectorIf is a three dimensional vector then

Addition of Vectors 

Scalar multiplication 

Negative of a vector 

Zero Vector

A Vector is called zero vector.

Unit Vector: A vector whose magnitude is 1.

.

.If is a vector then

unit vector is defined as

STANDARD UNIT VECTORS

0,0,1k and

0,1,0j

1,0,0i

.

Question No. 5If and Find the

(a) Component form and

(b) Magnitude(length) of the vector

2𝑢−3 𝑣

Exercise 12.2 Page No. 690

 

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A force of 6 newtons is applied in the directionof the vector . Express the force as a product of its magnitude and direction.

Example 6 Page No. 688