1. Vectors
Accelerated Math 3

2. Definitions and Properties (Pg. 453)
A Vector Quantity is a quantity, such as force, velocity or displacement, that has both magnitude (size) and direction.
A Scalar is a quantity, such as time, speed, or volume, that has only magnitude, no direction.
A Vector is a directed line segment that represents a vector quantity. Symbol:
The Tail of a vector is the point where it begins. The Head of a vector is the point where it ends. An arrowhead is drawn at the head of a vector.

3. Definitions and Properties (Pg. 453)
The Magnitude, or absolute value, of a vector is its
length. Symbol: If
A Unit Vector is a vector that is 1 unit long. Vectors
are unit vectors in the x-and y-directions,
respectively. A unit vector in the direction of a
given vector is found by
Two vectors are Equal if they have the same magnitude and direction. So you can Translate a vector without changing it, but you can’t rotate or dilate it.

4. Definitions and Properties (Pg. 453)
The Opposite of a vector is a vector of the same length in opposite direction. Symbol:
A Position Vector, , starts at the origin and ends at the point (x,y).
A Displacement Vector is the difference between an object’s initial and final positions.

5. Ex. 1 (Pg. 455) a) Write these vectors in terms of their components.
b) Translate so that its tail is at the head of Then draw the resultant vector Find numerically by adding the components of and , and show that the answer agrees with your drawing.

6. Ex. 1 (Pg. 455) c) How would you find ?
Why is the answer equivalent to ?
d) Find , and Based on the graph,
explain why

7. Ex. 2 (Pg. 456) a)Draw as a position vector.
Then translate so that the tail
is at the head of Using the
definition of vector addition draw
. Explain why is equivalent to .

8. Ex. 2 (Pg. 456) b) Draw a displacement vector
from the head of to the head of
. Explain why this vector is
equivalent to from part a.

9. Ex. 2 (Pg. 456) c) Find numerically from the coordinates of and , and
show that the answer agrees with
your drawings in parts a and b.