6.3 Vectors in the plane Day 1 Objectives: - define vectors - identify

component form of a vector

- calculate the magnitude of a vector

Warm UpFind the distance

between the following two points

(5 , 1) & (-2 , 6)

Vectors in the plane

Definition: A vector is a quantity possessing

magnitude AND directionExamples:Velocity, acceleration, magnetic fields,

force, etc. A scalar is a quantity with only

magnitudei.e. Speed vs. Velocity

Vectors in the plane

Vectors are usually visualized as a directed line segment or ray on a coordinate plane.

It’s direction goes from an initial point to a terminal point.

Vectors in the plane

Note: a vector in standard position has its initial point at the origin.

Vectors in the plane

The component form of a vector PQ with initial point (p1 , p2) and terminal point (q1 , q2) is

< q1 - p1 , q2 - p2 > which can also be written

as < v1 , v2 >

Which can also be written as v or

v

Vectors in the plane

A vectors magnitude is its length

The magnitude of a vector is denoted by

v

Vectors in the planeThe magnitude of a vector is

Which also equals

v

2 21 1 2 2( ) ( )v q p q p

2 21 2( ) ( )v v

Vectors in the plane

If = 1, then we call the vector a unit vector ( kind of like the unit circle has radius = 1)

v

Vectors in the plane Example 1:Find the component form and magnitude

of if its initial side is P(3 , -5) and terminal side Q(-2, 7)

v

HOMEWORK

P. 453 # 3-13 ODD