Recently, I found an equationr(s,t)=r0+ sv+ tw ,which is a plane with a point and two vectors lying on it.

I don't know why this is an equation of a plane.

can anyone teach me how to interpret r(s,t)= r0 + sv + tw ?

and

is there a method to convertinto the formr(s,t)= (-3,4,-9) +s(9,-5,9) + t(3,-2,3)(r-=0?r0).n

Thank you.