A Level Maths Notes: C4 – Finding the Vector Equation of a Line Passing Through Two Given Points
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:
