Introduction to Vectors Lesson 10.3

Scalars vs. Vectors Scalars Vectors Quantities that have size but no direction Examples: volume, mass, distance, temp Vectors Quantities that have both size and direction Examples Force Velocity Magnetic fields Size Terminal point Initial point

Vectors Representation Magnitude of a vector Equivalent vectors B Representation Boldface letters n or S Letters with arrows over them Magnitude of a vector Length of the vector, always positive Designated |K| Equivalent vectors Same magnitude and Same direction C

Resultant Vectors Given vectors The resultant vector (of both vectors added together) is vector We say Note that this is the diagonal of a parallelogram Can be determined by trigonometric methods D B

Vector Subtraction The negative of a vector is a vector with … So The same magnitude The opposite direction So - V V P Q S T

Try It Out Given vectors shown Sketch specified resultant vectors A F B

Also called "resolving" a vector Component Vectors Any vector can be represented as the sum of two other vectors Usually we represent a vector as components of a horizontal and a vertical vector Also called "resolving" a vector

Position Vector Given a point P in the coordinate plane Then is the position vector for point P Component vectors determined by Px = |P| cos θ Py = |P| sin θ • P (x,y) θ O

Finding Components Given a vector with magnitude 16 and θ = 212° What are the components? θ = 212° 16

Application A cable supporting a tower exerts a force of 723N at an angle of 52.7° Resolve this force into its vertical and horizontal components Vx = _______ Vy = _______ 723N 52.7°

Magnitude and Direction Given horizontal and vertical components Vx and Vy Magnitude found using distance formula Direction, θRef, found with arctan

How Magnitudinous It Is Given vector B with Bx = 10 and By = -24 Determine magnitude and reference angle. θ = ? |B| = ?

Assignment Lesson 10.3 Page 420 Exercises 1 – 35 odd