8.2 Algebraic vectors.notebook

8.2 Algebraic vectors.notebook
February 28, 2013
L.T. : Add andsubtract vectors geometrically.
1
8.2 Algebraic vectors.notebook
February 28, 2013
2
8.2 Algebraic vectors.notebook
February 28, 2013
L.T. : Find ordered pairs that represent vectors. Add, subtract
multiply and find the magnitude of vectors algebraically.
8.2 Algebraic Vectors
Put in standard position
v = h = AB =
|AB| =
Let P1(x1 , y1) be the initial point of a vector and P2
(x2 , y2) be the terminal point. The ordered pair
P1P2 is <x2 x1 , y2 y1>
Magnitude |P1P2| = √(x2 x1)2 + (y2 y1)2
Example: Write the ordered pair that represents the vector from C(7, 3) to D(2, 1). Then find the magnitude of CD.
3
8.2 Algebraic vectors.notebook
February 28, 2013
Adding/Subtracting/Multiplying vectors
u = <1, 4> v = <0, 8>
a. u + v
b. 2u + 1/2v
c. u v
4
8.2 Algebraic vectors.notebook
February 28, 2013
unit vector: a vector that has magnitude of one unit. i = <1, 0> and j = <0, 1>
Any vector that is written as an ordered pair can be written as the sum of unit vectors.
Example: Write AB as the sum of unit vectors for A (2, 7) and B(1, 5)
Vector NotationSum of unit vectors
Find the magnitude and direction of AB
5
8.2 Algebraic vectors.notebook
February 28, 2013
Example:
A recently built world class cruise ship stretches 964.5 feet in length. Suppose that the ship leaves port and sails for 80 miles in a direction of 50 degrees north of due east(E50N). Draw a picture and find the magnitude of the vertical and horizontal components.
6

Download Report