### Adding vectors: A + B

Physics
Chapter 4
• Working With Vectors
A
B
A+B
Draw the first vector listed.
Then draw the second
vector, placing the tail on
the head of the first one.
Then draw a line from the
tail of the first to the head
of the last.
B
A
A+B
A+B+C
A
B
C
Draw the first vector listed.
Then draw the second
vector, placing the tail on
the head of the first one.
B
A
C
Repeat with the next one.
A+B+C
Then draw a line from the
tail of the first to the head
of the last.
This can be done with many
vectors!
A+B+C+D+E
C
A
D
B
E
A+B+C+D+E
B
A
C
D
E
Subtracting vectors:
A
B
A-B
Draw the first vector listed.
Then draw the second
vector reversed, placing
what was the tail on the
Then draw a line from the
tail of the first to the head
of the last.
-B
A
A-B
A
B
B-A
Draw the first vector listed.
Then draw the second
vector, placing the tail on
the head of the first one.
Then draw a line from the
tail of the first to the head
of the last.
B
-A
B-A
What do you notice about these two?
A
B
B
A
-A
B–A
-B
A–B
What do you notice about these two?
A
B
B
A
A+B
B+A
A
B
Multiplying vectors:
3A
and
-2 B
A
B
3A
-2B
3A – 2B
A
B
-2B
3A
3A – 2B