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

A Vector is a directed line segment that A Vector is a directed line segment that has two has two and only two and only two defining defining

characteristics:characteristics:

Magnitude : size/lengthDirection: 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

ComponentsComponentsVectors 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 Find the horizontal and vertical components of the vector:components of the vector:

Find the horizontal and vertical Find the horizontal and vertical components of the vector: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:

v = 2, 3

Vector OperationsVector OperationsTo add vectors in component form, just add the

horizontal components and the vertical components.

1 1 2 2,u v u v u v

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.

15,3

5

,4

43, 6,71

u v

u v