1. Position Vectors Distance between 2 points

2. 2D Position Vectors - 1
The displacement of an object from the origin is called it’s Position Vector R O r OR
Every point has a unique position vector

3. 2D Position Vectors - 2 R A position vector is r fixed to the origin O
A free vector has magnitude and direction, but is not fixed to the origin s

4. r + s = t s = t - r Position Vectors – example 1 R r O s t T
What is the displacement from R to T?
r + s = t O
s = t - r t T

5. A a = xi + yj + zk 3D Position Vectors z a y o x
Similarly in 3D, all points
have position vectors a y
e.g. The position vector of point A o
a = xi + yj + zk x

6. a + = b = b - a Distance between 2 points B A |AB| = (52 + 52 + 82) z
A and B have position vectors x y z b B
What is the distance between them? AB a A
a = b AB AB
= b - a
|AB| = ( )
= 114 = 10.7 AB

7. = b - a Distance between 2 points - general case B A
A and B have position vectors x y z B b
What is the distance between them? A a AB
= b - a AB
|AB| = (x2-x1)2 + (y2-y1)2 + (z2-z1)2