This document provides an overview of vectors as covered in Lesson 1 of Module 1 of a Calculus III textbook. It defines vectors, their components, magnitude, addition, scalar multiplication, unit vectors, and standard unit vectors. It also includes two example problems, one calculating the components and magnitude of the vector 2u - 3v, and another expressing a force vector as the product of its magnitude and direction.

1. Math 301[Calculus-III]
Text Book:
Thomas Calculus Early Transcendental
Edition: 12
Publisher: Pearson

2. VECTORS
Exercise 12.2
Page 690
Module - I

3. 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

6. 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

7. Vector:

9. Component of a Vector
If , are the points then
position vector equal to is

10. Magnitude of a Vector
If is a three dimensional vector then

11. Addition of Vectors

12. Scalar multiplication

13. Negative of a vector
Zero Vector
A Vector is called zero vector.

14. Unit Vector: A vector whose magnitude is 1.
.
.
If
is a vector then
unit vector is defined as

15. STANDARD UNIT
VECTORS



0,0,1k
and
0,1,0j
1,0,0i







16. .
Question No. 5
If 𝑢 =< 3 , −2 > and 𝑣 =< −2 , 5 > . Find the
(a) Component form and
(b) Magnitude(length) of the vector
2𝑢 − 3 𝑣
Exercise 12.2 Page No. 690

17. .

18. A force of 6 newtons is applied in the direction
of the vector 𝑣 = 2 𝑖 + 2 𝑗 − 𝑘. Express the force
𝐹 as a product of its magnitude and direction.
Example 6 Page No. 688