Okay so I read about the equation of a plane that is parallel to 2 vectors and passes through a point(say 'P').

And i am thinking, if we have 2 vectors to which the plane is parallel, why do we need another point? Or should that point be a parameter in determining the equation of a plane.

So I argue that there must be two cases:-

1) The plane that contains the 2 vectors to which it is parallel does not contain the point P - possible and absurd. Say the plane is parallel to

and

and I want it to pass through say (0,0,4). I cannot have such a plane.

(2) So the point has to lie on that plane. Say the vectors are ~a and ~b . So the k

_{1}a + k

_{2}b gives us the entire plane for different values og k1 and k2.

My question is that if it also has to pass through P (with ~OP=P) isn't k

_{1}a + k

_{2}b a sufficient equation ? I think so.

But my book says differently. It says that the equation will become P+k

_{1}a + k

_{2}b .

Please help !