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Section03

Section03 - Physics 204A Class Notes Section 3 Vectors...

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Physics 204A Class Notes 3-1 Section 3 – Vectors Section Outline 1. Vectors 2. Components of a Vector 3. Addition of Vectors 4. Multiplication of Vectors Vectors are a mathematical tool. Like all math tools, they seem unnecessarily difficult and not too helpful at first. However, after they have been mastered, they turn out to be a great convenience. 1. Vectors Scalar: A quantity with a magnitude only. Vector: A quantity with magnitude and direction. Example 3.1: A hiker walks 20.0m NNE. Sketch this vector. The vector as shown at the right. The length of the vector is proportional to the magnitude (20.0m) and the arrow indicates the direction. Note that vectors can be moved with respect to the origin as long as neither the magnitude nor direction is changed. A way to right this vector is, r r = [email protected]˚ N of E . This method is cumbersome. We will learn a better way soon. Note: The book uses bold type face for vectors ( r = r r ). 2. Components of a Vector Example 3.2: A hiker walks 20.0m NNE. Find the distance she has gone northward and the distance eastward. Convert these polar coordinates to Cartesian, y = r sin ! = 20.0sin67.5˚ " y = 18.5m northward and x = r cos ! = 20.0cos67.5˚ " x = 7.65m eastward . These parts of the vector are called “components.” Unit Vectors: ˆ i 1 unit along the x-axis, ˆ j 1 unit along the y-axis and ˆ k 1 unit along the z-axis.

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