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CHAPTER-6 for Remedial Program (1).pptx of basic mathematics
- 1. College of Naturaland 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 ScalarMultiplication 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.
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- 21. Cross product ofvectors
- 25. Transformation of theplane (Reflection, Translation, Rotation)
- 26. Cont. There are threetypes of rigid motions (transformations) these are I. Translations II. Reflections III. Rotations.
- 27. Translation Definition If everypoint 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).
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- 33. Reflection in theline y = mx, where m = tan θ • Expanding (2 – ) and (2 – ). Now, using these 𝑐𝑜𝑠 𝜃 𝛼 𝑠𝑠𝑖𝑛 𝜃 𝛼 trigonometric identities, you obtain:
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- 35. Reflection in theline y = mx + b
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