UNIT SIX LESSON TWO
Lesson Two: Vector Addition
When we add and subtract vectors, it will be important to know the angle that the vectors make with
eachother. NOTE: The angle between two vectors is ALWAYS measured between their TAILS.

The sum of two vectors is often called the RESULTANT vector. The notation is R .
TRIANGLE LAW OF ADDITION OF VECTORS:
1.
2.
Translate the two vectors so that the tail of the first vector is positioned at the head of the second
vector.

R is the vector that shares its initial point with the first vector and its terminal point with the second
vector.
PARALLELOGRAM LAW OF ADDITION OF VECTORS:
1.
Translate the two vectors so that their tails are together.
2.
Draw a parallelogram using these vectors as adjacent sides.

R is the diagonal that has the same tail as the original vectors.
3.




Ex. Given two vectors, a and b such that a  10 m and b  12 m, and the angle between them is 45, find
 
a  b.
SUBTRACTION
OF
 VECTORS: Subtraction of vectors is defined as adding a vector in the opposite direction.
  
i.e., a  b  a   b . Then we apply the triangle law, or parallelogram law of addition.
 
UNIT SIX LESSON TWO

Zero Vector: 0 , or the zero vector, is a vector that starts and ends at the same point. It has an undefined

direction and a magnitude of zero. i.e., 0  0
Ex.

a

b
  
ab  0
Ex.
A
C
B

 

AB  BC  C A  0

 
Ex. Using the diagram below, express the following vectors in terms of i , j , and k .
A
C
B
D

k
G

i
E

j
F
H
UNIT SIX LESSON TWO