CHAPTER-6 for Remedial Program (1).pptx of basic mathematics

Freshaan course of basic mathematics

1. College of Natural and Computational Sciences Department of Mathematics Compiled Mathematics Module for Natural Science Pre-University Remedial students

2. Chapter Five Vectors Definition : A physical quantity which has magnitude but not direction is called a scalar. Example: speed, distance, temperature, etc. Definition : A physical quantity which has both magnitude and direction is called a vector. Example : velocity, acceleration, force, etc. Notation : Vectors are mostly denoted by bold letters or arrow headed letters and in this chapter they are denoted by bold letters like u , v and w .

3. Addition and Scalar Multiplication of Vectors Definition : If u and v are vectors positioned so that the initial point of v is at the terminal point of u, then the sum u + v is the vector from the initial point of u to the terminal point of v.

4. Dot (Scalar) Product

5. Cross product of vectors

6. Transformation of the plane (Reflection, Translation, Rotation)

7. Cont. There are three types of rigid motions (transformations ) these are Translations Reflections Rotations .

8. Translation Definition If every point of a figure is moved along the same direction through the same distance, then the transformation is called a translation or parallel movement . If point P is translated to point P ', then the vector PP ‘ is said to be the translation vector . If u = ( h, k ) is a translation vector, then the image of the point P( x, y ) under the translation will be the point P′( x + h, y + k ).

9. Cont.

10. Cont.

11. Reflections

12. Cont.

13. Cont.

14. Reflection in the line y = mx, where m = tan θ Expanding 𝑐𝑜𝑠(2 𝜃–𝛼 ) and 𝑠𝑠𝑖𝑛 (2𝜃 –𝛼 ). Now, using these trigonometric identities, you obtain:

15. Cont.

16. Reflection in the line y = mx + b

17. Cont.

18. Cont.

19. Rotations

20. Cont.

21. Cont.

22. Cont.

23. Cont.

24. Cont.

25. Cont.

26. Cont.