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Chapter_3_Vectors

# Chapter_3_Vectors - Vectors What are they and how do we...

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Unformatted text preview: Vectors! What are they and how do we work with them? Vectors Vs. Scalars! • Unlike in real estate, with vectors it is not so much Location, Location, Location, but Direction, Direction, Direction! • Vectors have a length or magnitude and a direction. • Scalars are just a number. No direction! Examples Vectors Scalars • Wind • Market Trends? • A moving Walkway? • Mass • Cost • Calories Math • Scalar Math is the Math you knew in 5th grade • Vector Math is different, but NOT HARD! • Addition is addition • Vector Math can be done with real objects! • Multiplication is Multiplication • Vector Math is Pictures! Vector Addition + = - = The Negative of a Vector =- Notice the Length does not change, and the direction is exactly opposite! Multiplying a Vector by a scalar! X2= Notice the direction does not change! Vector Components! • Vectors can be broken into components! • Most often these components are perpendicular! (not always) • Think of it as taking steps along the x, y, and z axis! Example = α + Note: Trigonometry can be used to find the length of the components if the angle α is known! In this case the length of = the length of X sin(α) And the length of = the length of X cos(α) Unit Vectors • A Unit Vector is any vector that has a length of 1 unit (could be m or m/s etc.) in any direction! • Unit vectors along a coordinate axis are usually given special symbols • A simple way to write out a vector in terms of its components along the coordinate axis is to write the vector as the addition of unit vectors multiplied by scalars Questions on Vectors? Sweet! Quiz Time! Big Honking Laser! ...
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Chapter_3_Vectors - Vectors What are they and how do we...

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