Presentation on theme: "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."— Presentation transcript:
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. Its 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 (p 1, p 2 ) and terminal point (q 1, q 2 ) is which can also be written as 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)