Lesson 8-2

Example 1
Write the ordered pair that represents the vector from X(-2, 4) to Y(4, -6). Then find the magnitude of .

First, represent as an ordered pair.	

 = 4 - (-2), -6 - 4 or 6, -10

Then, determine the magnitude of .

||	= 
	=  or 2

is represented by the ordered pair 6, -10 and has a magnitude of 2 units.

Example 2
Let  = 2, -3,  = 1, 5, and  = -2, 4. Find each of the following.

a.	 + 
 + 	= 1, 5 + -2, 4
	= 1 + (-2), 5 + 4
	= -1, 9	b.	 - 
 - 	= 2, -3 - -2, 4
	= 2 - (-2), -3 - 4
	= 4, -7	
		
c.	3
3	= 31, 5
	= 3  1, 3  5
	= 3, 15	d.	2 + 3
2 + 3	= 22, -3 + 3-2, 4
	= 4, -6 + -6, 12
	= -2, 6	

Example 3
EMERGENCY MEDICINE  Two paramedics are moving a person on a stretcher. Bob is pushing the stretcher with a force of 120 Newtons at 50 with the horizontal, while Ed is pulling the stretcher with a force of 200 Newtons at 40 with the horizontal. What is the magnitude of the force exerted on the stretcher?

Draw a diagram of the situation. Let	
 represent the force Bob exerts
and let  represent the force Ed
exerts.

Write each vector as an ordered pair
by finding its horizontal and vertical
components. Let  and  represent the x and y components of  and let  and  represent the x and y components of .

	cos 50°	= 
	||	= 120 cos 50°
		 77.1

	sin 50°	= 
	||	= 120 sin 50°
		 91.9	
	cos 40°	= 
	||	= 200 cos 40°
		 153.2

	sin 40°	= 
	||	= 200 sin 40°
		 128.6	

Find the sum of the vectors.

 + 	 77.1, 91.9 + 153.2, 128.6
	 230.3, 220.5

The net force on the stretcher is the magnitude of the sum.

| + |   or about 319

The net force on the stretcher is about 319 Newtons.

Example 4
Write  as the sum of unit vectors for A(3, -2) and B(7, 4).

First, write  as an ordered pair.	

	= 7 - 3, 4 - (-2)
	= 4, 6

Then write  as the sum of unit vectors.
 = 4 + 6