8.3a-Vectors Terms Operations Practice Problems

What are Vectors Used For?  Vectors represent  Paths of travel i.e. distances  Velocity Direction and speed of an object  Forces Weight Pressure 2

Terms  Vector  Directed line segment Similar to a line or ray  Has direction Can be designated by: Ordered pairs Radians Degrees Graphically 3

Terms (Cont.)  Vector (Cont.)  Has Magnitude How long the vector is Basically, the hypotenuse of a triangle if it is not purely vertical or horizontal 4

Notation  Ordered Pair Form  Same as ordered pairs except <> is used instead of () 5

Notation (Cont.)  Vector Name  When possible use named points Starting point is listed 1 st Ending point is listed 2 nd Arrow is placed over the letters Ex.  If no named points are available, “u” and “v” are typical 6

Notation (Cont.)  Vector Example 7

Notation (Cont.)  Magnitude  Amount of force, weight, velocity, etc.  Represented by: Vector Name Enclosed by double vertical lines 8

Addition/Subtraction of Vectors  Combines the elements of 2 or more vectors  Result is called a Resultant Vector 9

Graphic Representation of Vector Addition/Subtraction  Align vectors end-to-end without changing the angle  Draw a new vector from the beginning of the first vector to the end of the last vector  Name the resultant vector according to beginning and ending points 10

Graphic Example of Addition of Vectors 11

Scalar Multiples  Changes the magnitude  But not the angle  Steps  Multiply each component of the vector by the scalar (number) 12

Scalar Multiples Examples 13

Finding the Magnitude  Steps  Square each element of the vector  Add  Take the square root  Basically the Pythagorean Theorem 14

Finding the Magnitude (Cont.) Find the Magnitude of 15

i & j Coordinate System In plain English… i is the x-axis, and j is the y-axis 16

i and j Coordinate Example  Treat i and j as if they were variables 17

Practice Problems  Page 601 Problems 1-10,