Exercise 12.2
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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.
![Math 301[Calculus-III]
Text Book:
Thomas Calculus Early Transcendental
Edition: 12
Publisher: Pearson](https://image.slidesharecdn.com/exercise12-151020013920-lva1-app6891/85/Exercise-12-2-1-320.jpg)
Exercise 12.2
- 1. Math 301[Calculus-III] Text Book: Thomas Calculus Early Transcendental Edition: 12 Publisher: Pearson
- 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
- 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
- 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