6.3 Vectors in the plane Day 1 Objectives: - define vectors - identify component form of a vector - calculate the magnitude of a vector Warm Up Find the distance between the following two points (5 , 1) & (-2 , 6)

Vectors in the plane Definition: A vector is a quantity possessing magnitude AND direction Examples: Velocity, acceleration, magnetic fields, force, etc. A scalar is a quantity with only magnitude i.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

Vectors in the plane A vectors magnitude is its length The magnitude of a vector is denoted by

Vectors in the plane The magnitude of a vector is Which also equals

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

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)

HOMEWORK P. 453 # 3-13 ODD