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LG 4-3 Vectors Today: Notes Tomorrow: Practice Operations (I will not be here!) Friday: Practice Monday: Review and Test

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Unit 5: Non-Cartesian Functions LG 5-1: Vector Functions (quiz 10/14) LG 5-2: Parametric Functions (quiz 10/16) LG 5-3: Polar Functions (quiz 10/18) TEST 10/21

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A Vector is a directed line segment that has two and only two defining characteristics: Magnitude : size/length Magnitude Direction: direction from one place to another (has 2 parts – an angle and a cardinal direction) The notation of a vector is a single letter in bold (v or u, etc) or a single letter with an arrow on top

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Components Vectors are made up of the Horizontal (x) and Vertical (y) Components Express the vector coordinates below as ordered pairs in simplest radical form.

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Find the horizontal and vertical components of the vector:

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If a position vector has length 8 cm and direction 60°SW, then find the horizontal & vertical components.

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Find the magnitude and direction of the vector: v = 2, 3

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Magnitude of a Vector: Direction of a Vector:

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Vector Operations To add vectors in component form, just add the horizontal components and the vertical components. To add vectors graphically, just play “follow the leader.” Then draw a new vector from the start of the first to the end of the second. The new vector is called the resultant or displacement vector.

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To make a negative vector (for subtraction) just distribute a negative. Graphically, you have the same slope and magnitude. You just go in the opposite direction. To multiply a vector by a scalar (constant), just distribute the number to both coordinates. Graphically, you make the vector that many times as long in the same direction

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A Bigger Example 2u -3v

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If u = 2, 3 & v = 1, 2 , find 2u + 3v.

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