Section 9.1: Vectors in the Plane
A vector in R2 has two components.
It expresses magnitude and direction.
Imagine an arrow with terminal and initial points.
The vector from (1,2) to (4,8) is
< 3, 6 >
It can also be written 3i + 6j
(4,8)
(1,2)
A “regular old number” is called a scalar.
We can add vectors and multiply by scalars.
 3, 6    5,  7    2, 13 
(3i + 6j ) - (5i - 7j) = -2i + 13j
4  3, 6    12, 24 
The norm of a vector is its length.
||  3, 6  || 
3  6
2
2

45
A unit vector has length 1.
3
6
,
45 45
is a unit vector in same direction as  3, 6 
In a scene from Muppet Treasure Island,
Clueless Morgan & Polly Lobster pull Gonzo’s arms
with a force of <3, 6> N and <5, -9> N, respectively.
The force on Gonzo is
<3, 6> + <5, -9> = <8, -3> N