Characteristics, Properties & Mathematical Functions Vector Basics Characteristics, Properties & Mathematical Functions

What is a Vector? Any value that requires a magnitude and direction. Examples we have already used this year Velocity Displacement Acceleration New example Force: a push or pull on an object unit: Newton (N)

How to show a Vector? Drawn as an arrow Length represents the magnitude of the vector. Arrow points in the correct direction. Individual vectors are called COMPONENTS The sum of 2 or more vectors is called a RESULTANT. (A resultant is one vector that represents all the components combined.)

Representing Direction Draw the arrow pointing in the correct direction. North North is up South is down East is right West is left West East South

Vector in One Dimension So far we have only dealt with vectors on the same plane. Walk 10m to the right and then 5 m more to the right = 10 m + 5 m 15 m When 2 vectors are in the same direction add the values and keep the same direction!

Vector in One Dimension Walk 10m to the right and then 5 m to the left - 5 m = 10 m 5 m When 2 vectors are in opposite directions subtract the values and keep the direction of the bigger value.

Between the basic directions If your vector is exactly between 2 basics directions both will be named. Northeast Southeast Northwest Southwest N W E S

Direction not exactly between Start pointing toward the last written direction. Turn the number of degrees given toward the 1st written direction. For example: 30˚ north of west Start west and turn 30˚to north N W E S

Direction not exactly between Start pointing toward the last written direction. Turn the number of degrees given toward the 1st written direction. For example: 55˚ south of east Start east and turn 55˚to south N W E S

= Vectors in 2 Dimensions + Vectors that are in two different directions that meet at a 900 angle to each other requires the use of Pythagorean theorem and trigonometric functions. 5 m + 4 m = 53° N of E 3 m

a2+b2=c2 SOH CAH TOA Sin A = a/c Cos A =b/c Tan A = a/b Right Triangles a2+b2=c2 SOH CAH TOA Sin A = a/c Cos A =b/c Tan A = a/b

(3m)2 + (4m)2 =R2 R = 5m Tan θ= 4m/3m Tan-1(4/3) θ=53°N of E Pythagorean Theorem (3m)2 + (4m)2 =R2 R = 5m Tan θ= 4m/3m Tan-1(4/3) θ=53°N of E