Calculating the intercepts of a plane

[Brewer]

Homework Statement

The actual question relates to Miller indicies, but I can do that part of it. I just can't remember how you figure out where the plane crosses each axis when you have 3 points. For example in my question the plane crosses through (1,1,1) (1,0,0) and (0,0,1). However I can't figure out where the plane will cross the axes. Can anyone tell me how I work this out (a general case, so it can be applied to any points).

Thanks

 

[stunner5000pt]

find the equation of the plane - for this you need 2 unique direction vectors and a point through which the plane passes.

you can find the direction vectors by finding the vectors between the points on given plane

then any points which lies on your plane is given by

$$(x,y,z) = (x_{0},y_{0},z_{0}) + sd_{1} + td_{2}$$

where s and t are any real number

fidning the intercepts from this point is pretty straightforward

 

[Brewer]

Thank you. I do remember it now - its been a few years, but I remember it.