# Vector equation of a plane

#### Skelly4444

##### Junior Member
Please can someone tell me if there's a set procedure for obtaining a vector equation of a plane in the form a = bd1 + cd2, if you're given the Cartesian form of the equation? The example in my further maths book doesn't work when I apply it to a different question. Surely there's a tried and tested method for converting from Cartesian form?

I can successfully do it if it's the other way round and I am converting it into a Cartesian equation.

Please can someone tell me if there's a set procedure for obtaining a vector equation of a plane in the form a = bd1 + cd2, if you're given the Cartesian form of the equation? The example in my further maths book doesn't work when I apply it to a different question. Surely there's a tried and tested method for converting from Cartesian form?

I can successfully do it if it's the other way round and I am converting it into a Cartesian equation.

First find [imath]\mathbf p[/imath] such that [imath]\mathbf p\cdot \mathbf n = d[/imath]. There many solutions to this (the whole plane as a matter of fact ), so you can just use a scaled version of [imath]\mathbf n[/imath], i.e. $\mathbf p = \frac{d}{||\mathbf n||^2} \mathbf n$