Equation of a plane parallel on a line

Question

I need some help: So: A2 is a plane, I know 1 point ( M(3,-4,2) ) from plane and 1 direction vector ( (2,1,-5) ) (from A1 ) but i need one more direction vector.How can I use that parallelism information? I know that normal vector of A2 * director vector of A'1 = 0 (dot product) but how can I use this? img

Answer 1

There are many ways you can find the plane you seek, for example, since $A_1$ is contained in your plane, you can use it to find a vector $v$ defined by two of its points (you can choose them arbitrarily). Then, using $M$ as base point, the vectorial equation of the plane will be $X=M+ \lambda.v + \mu.(2,1,-5)$.

Of course you can get around this in other ways, but this one will do the trick.