–
form of a line as something like
or
but
expressions like these are not possible in three dimensions. We go
right back to the vector form, and start by identifying
the
and
components:
A Level Maths Notes: C4 – Changing Between Cartesian and Vector Forms of Equations of Lines in Three Dimensions
You may be used to seeing the cartesian ––
form of a line as something likeor
but
expressions like these are not possible in three dimensions. We go
right back to the vector form, and start by identifying
theandcomponents:
Hence
For
each of these three components we make the parameter
the subject:
Each of these expressions are equal to
so
they are all equal to each other:
This expression is the cartesian form of a line in three dimensions.
Conversely, given the cartesian form of a line we can write out down the vector form:
Each term is not constant sinceandare
variables, so put them equal to a common parameter
and
write down separate equations for each component, solving them
forand
Then