1. 8-5 Vectors Part 2: Adding and Applications

2. Resultants Vectors can also be named with a single lowercase letter, such as u. The map shows vectors representing a flight from Albuquerque to Salt Lake City, with a stopover in Flagstaff. The vector from Albuquerque to Salt Lake City is the sum, or resultant, of the other two vectors. – This is written as w = u + v.

3. Adding Vectors For a =  x 1, y 1  and c =  x 2, y 2 , a + c =  x 1 + x 2, y 1 + y 2 . Given vectors a =  -4, -3  and c =  1, -2 , what is the resultant e of the two vectors as an ordered pair? Draw the resultant.

4.  What is the resultant of  2, 3  and  -4, -2  as an ordered pair?

5. Vector Applications A vector sum can show what happens when vectors occur in sequence, as in the plane flight described previously. A vector sum can also show what happens when vectors act at the same time. – When you row a boat, for example, the current may affect the direction you need to paddle to get to your destination.

6. Applying Vectors Your friend invites you to go boating on the river. The speed of the powerboat in still water is 35 mph. The river flows directly south at 8 mph. If the powerboat heads directly west, what are the boat’s approximate resultant speed and direction?  At what angle should the powerboat head up river in order to travel directly west?

7.  A ship begins a cruise and docks 120 miles east and 45 miles south of where it began. The result of the trip can be described by the vector  120, -45 . What are the magnitude and direction of the trip vector?