The general equation of a line passing through two points
and
is given by
where
andcan be in two or three dimension ie
or
t is a parameter – the value of
determines a unique point on the line. Any point on the line can be found by substituting a suitable value of
The pointsandmay be expressed in two different forms, but both forms label the same point in space:
is equivalent to the vector
is equivalent to the column vector
Example: Find the equation of the line passing through the the points
and
If instead of
component form we used column vector form we word have
(1)
The two forms are equivalent, which can be seen from (1) by writing
So that
Conversely we can change from column vector form to component form:
