12 A VECTORS AND SCALARS 12 B GEOMETRIC OPERATIONS HOMEWORK: VIEW POWER POINT BEFORE NEXT CLASS

12A VECTORS AND SCALARS

12A: VECTORS AND SCALARS  Scalars – quantities that only have one magnitude  Examples: speed of a plane  Vectors – quantities that have both magnitude and direction  Examples: velocity of a plane, acceleration, force, displacement, momentum  Represented by a direct line segment or arrow  The length of the arrow represents the size or magnitude of the quantity and the arrowhead shows the direction.

EXAMPLE 1

VECTOR NOTATION

GEOMETRIC NEGATIVE VECTORS

GEOMETRIC VECTOR EQUALITY Two vectors are equal if they have the same magnitude and direction. Equal vectors are parallel and in the same direction, and are equal in length. Given a magnitude and direction, vectors can be drawn from any point.

EXAMPLE 2

12B GEOMETRIC OPERATIONS WITH VECTORS

GEOMETRIC VECTOR ADDITION

STEPS FOR CONSTRUCTING VECTOR ADDITION

THE ZERO VECTOR

EXAMPLE 4

GEOMETRIC VECTOR SUBTRACTION To subtract one vector from another, add its negative.

EXAMPLE 5

EXAMPLE 6

VECTOR EQUATIONS Given a closed polygon, you can write a vector equation which relates vectors. There are multiple ways to write equivalent equations.

EXAMPLE 8

GEOMETRIC SCALAR MULTIPLICATION

EXAMPLE 9

EXAMPLE 10

NEXT CLASS There will be time for questions over these slides. However, you must do your best to follow the material before next class. You will work on homework during class (flipped classroom).