A.) Scalar - A single number which is used to represent a quantity indicating magnitude or size. B.) Vector - A representation of certain quantities which have both a magnitude and a direction. For example, force, velocity, and acceleration are all vector quantities

C.) Notation - The following is vector PQ, notated by With initial point P and terminal point Q. P Q We can also notate the vector with one letter v.

D.) Vector Magnitude- = length/magnitude of the vector 2 vectors are equivalent iff their length and direction are the same. (Note: Location in the plane does not matter.) For example,

E.) Ex. 1- Let v be represented by the directed line segment from R = (0,0) to S = (-8, -15) and u is represented by the directed line segment from Q = (-3, 4) to Z = (-11, -11). Prove v = u. A.) Direction: Does the slope of v = the slope of u? B.) Magnitude: Does | v | =| u |?

A.) Standard Position: Any vector with its initial point at the origin. -Every vector in the coordinate plane has an equivalent vector in standard position. B.) Component Form: any vector v in the plane equal to the vector with initial point (0, 0) and terminal point (v 1, v 2 ).

C.) Ex. 2- If and, then Called the “components”

D.) Magnitude in component form- given v = determined by and

E). Ex. 3- Find the component form and magnitude of the vector with

A.) Vector Addition – B.) Product of a vector and scalar -

C.) Ex. 4- Let. Find

A.) Any vector u with |u| = 1. If v is not the zero vector with no direction), is a unit vector in the direction of v.

B.) Ex. 5- Find the unit vector in the direction of

A.) Any vector can be written as an expression in terms of the standard unit vectors

A.) The acute angle θ makes with the positive x- axis. B.) Components Horizontal comp: Vertical comp:

B.) Ex. 6- Find the components of the vector v with a directional angle of 60º and a magnitude of º a b

C.) Ex. 7- Find the magnitude and directional angle of the vector