7.1. Basic Properties of Vectors http://www.ck12.org
−→AB=<− 5 ,− 9 >
−→BA=< 5 , 9 >
−→AC=< 4 ,− 16 >
CB−→=<− 9 , 7 >
Concept Problem Revisited
There are many differences between points and vectors. Points are locations and vectors are made up of distance
and angles. Parentheses are used for points and<>are used for vectors. One relationship between vectors and
points is that a point plus a vector will yield a new point. It is as if there is a starting place and then a vector tells
you where to go from that point. Without the starting point, the vector could start from anywhere.
Vocabulary
Avectoris a set of instructions indicating direction and magnitude.
Thetail of a vectoris the initial pointwhere the vector starts.
Thehead of a vectoris the terminal pointwhere it ends.
Aforce diagramis a collection of vectors that each represent a force like gravity or wind acting on an object.
Magnituderefers to the length of the vector and is associated with the strength of the force or the speed of the
object.
Bearingis measured with 0◦as due North, 90◦as East, 180◦as South and 270◦as West.
Guided Practice
- A father is pulling his daughter up a hill. The hill has a 20◦incline. The daughter is on a sled which sits on the
ground and has a rope that the father pulls as he walks. The rope makes a 39◦angle with the slope. Draw a force
diagram showing how these forces act on the daughter’s center of gravity:
a. The force of gravity.
b. The force holding the daughter in the sled to the ground.
c. The force pulling the daughter backwards down the slope.
d. The force of the father pulling the daughter up the slope. - Center the force diagram from the previous question into the origin and identify the angle between each consecu-
tive force vector. - Given the following vectors and point, compute the sum.
A= ( 1 , 3 ),−→v=< 4 , 8 >,−→u =<− 1 ,− 5 >
A+−→v+−→u=?
Answers: - The girl’s center of gravity is represented by the black dot. The force of gravity is the black arrow straight
down. The green arrow is gravity’s effect pulling the girl down the slope. The red arrow is gravity’s effect pulling
the girl straight into the slope. The blue arrow represents the force that the father is exerting as he pulls the girl up
the hill.