Introduction to Vectors Lesson 10 3 Scalars vs

Introduction to Vectors Lesson 10. 3

Scalars vs. Vectors • Scalars Quantities that have size but no direction § Examples: volume, mass, distance, temp § • Vectors Quantities that have both size and direction § Examples Size § • Force • Velocity • Magnetic fields Terminal point Initial point 2

Vectors • Representation B C 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 § 3

Resultant Vectors • Given vectors • The resultant vector (of both vectors added together) is vector A D B C • We say • Note that this is the diagonal of a parallelogram § Can be determined by trigonometric methods 4

Vector Subtraction • The negative of a vector is a vector with … The same magnitude § The opposite direction § -V V • So T P S Q 5

Try It Out • Given vectors shown • Sketch specified resultant vectors A F D E C B 6

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 7

Position Vector • Given a point P in the coordinate plane • P (x, y) θ O • Then is the position vector for point P • Component vectors determined by Px = |P| cos θ § Py = |P| sin θ § 8

Finding Components • Given a vector with magnitude 16 and θ = 212° § What are the components? θ = 212° 16 9

Application • A cable supporting a tower exerts a force of 723 N at an angle of 52. 7° • Resolve this force into its vertical and horizontal components § Vx = _______ § Vy = _______ 723 N 52. 7° 10

Magnitude and Direction • Given horizontal and vertical components Vx and Vy § Magnitude found using distance formula § Direction, θRef, found with arctan 11

How Magnitudinous It Is • Given vector B with Bx = 10 and By = -24 θ=? |B| = ? • Determine magnitude and reference angle. 12

Assignment • Lesson 10. 3 • Page 420 • Exercises 1 – 35 odd 13