INTRODUCTION SCALAR QUANTITIES: _______________________________________________________ VECTOR QUANTITIES: ________________________________________________________ Geometry: Line Segment Vector Magnitude only Magnitude and direction length
Vocabulary and Notation: Standard Position: Magnitude (____________) Amplitude /Direction Angle (____________) Bearing: Equal Vectors : Opposite Vectors: Zero Vector: Unit Vector: Initial point and terminal point (where arrow is) Initial point origin length Counter clockwise From the x-axis Clockwise from the North Same direction, same magnitude Same magnitude, opposite direction A B B A 0 magnitude called a point vector Length 1
Component Form: Horizontal = x Vertical = y chevrons
Component Form: Graphically count
Component Form: Numerically Vector has endpoints A ( 4, -6) and B ( -6, 1 ). Find the component form of Vector has component form and initial point A ( -3, -2) Find the terminal point. B(x,y)
Examples: A Sketch the vector A with Magnitude :50 mm Amplitude:θ = 20 o Sketch the vector B with Magnitude :70 mm Bearing:θ = 135 o Examples: B Protractor Skills: Measure the magnitude and amplitude.
DOT Paper Sketch the vector C with Initial point ( 0, 0 ) and Terminal point ( -3, 5 ) Find the component form of the vector. Sketch the vector D with Initial point ( 0, 0 ) and Terminal point ( 6, -2 ) Find the component form of the vector.
Examples: Sketch the vector E with Initial point ( 4, 5 ) and Terminal point ( -1, -3 ) Find the component form of the vector. Sketch the vector F with Initial point ( -2, -3 ) and Terminal point ( 4, 1 ) Find the component form of the vector.
Draw the vector in standard position. Standard Position: count numerically
Component Form: x y TRIG magnitude
Find the component from of a vector with Trig component form Standard component trig standard
Magnitude and Amplitude: Magnitude is the length of the vector. Amplitude θ is the direction angle - Rem: positive direction Rem: if x is negative add 180 o if y-only is negative add 360 o
Find the magnitude and amplitude of the vector:
Unit Vector in the direction of : To find the unit vector in the direction of Divide the vector by its magnitude.
Adding and Subtracting Vectors Protractor Skills: Adding: Heel to Toe a b a+b
DOT Paper Adding: Heel to Toe a b
Adding and Subtracting Vectors Protractor Skills: Subtracting: Toe to Toe - must point toward the subtracting vector a b a - b b - a