LG 4-3 Vectors Today: Notes Tomorrow: Practice Operations

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Presentation transcript:

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

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

Magnitude : size/length A Vector is a directed line segment that has two and only two defining characteristics: Magnitude : size/length 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 Vectors with the same properties are equal, even if they are not in the same location.

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

Find the horizontal and vertical components of the vector:

Find the horizontal and vertical components of the vector:

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

Find the magnitude and direction of the vector:

Magnitude of a Vector: Direction of a Vector:

The new vector is called the resultant or displacement vector. 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.

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 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.

A Bigger Example 2u -3v

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