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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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Presentation on theme: "LG 4-3 Vectors Today: Notes Tomorrow: Practice Operations (I will not be here!) Friday: Practice Monday: Review and Test."— Presentation transcript:

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

2 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

3 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

4 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.

5 Find the horizontal and vertical components of the vector:

6

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

8 Find the magnitude and direction of the vector: v =  2, 3 

9 Magnitude of a Vector: Direction of a Vector:

10 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.

11 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

12 A Bigger Example 2u -3v

13 If u =  2,  3  & v =   1, 2 , find 2u + 3v.


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