Presentation on theme: "6.3 Vectors in the plane Day 1 Objectives: - define vectors"— Presentation transcript:
16.3 Vectors in the plane Day 1 Objectives: - define vectors - identify component form of a vector- calculate the magnitude of a vectorWarm UpFind the distance between the following two points(5 , 1) & (-2 , 6)
2Vectors 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
3Vectors in the planeVectors 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.
4Vectors in the planeNote: a vector in standard position has its initial point at the origin.
5Vectors in the planeThe 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 writtenas < v1 , v2 >Which can also be written as v or
6Vectors in the plane A vectors magnitude is its length The magnitude of a vector is denoted by
7Vectors in the planeThe magnitude of a vector isWhich also equals
8Vectors in the planeIf = 1, then we call the vector a unit vector ( kind of like the unit circle has radius = 1)
9Vectors 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)