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# Exercise 12.2

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### Exercise 12.2

1. 1. Math 301[Calculus-III] Text Book: Thomas Calculus Early Transcendental Edition: 12 Publisher: Pearson
2. 2. VECTORS Exercise 12.2 Page 690 Module - I
3. 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
4. 4. 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
5. 5. Vector:
6. 6. Component of a Vector If , are the points then position vector equal to is
7. 7. Magnitude of a Vector If is a three dimensional vector then
9. 9. Scalar multiplication
10. 10. Negative of a vector Zero Vector A Vector is called zero vector.
11. 11. Unit Vector: A vector whose magnitude is 1. . . If is a vector then unit vector is defined as
12. 12. STANDARD UNIT VECTORS    0,0,1k and 0,1,0j 1,0,0i      
13. 13. . 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
14. 14. .
15. 15. 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