Maths Help. How do you find the vector equation of a plane given 2 vectors contained in the plane and a point?

I am having trouble with the following maths problem.



How do you write in vector, parametric and cartesian form the plane through the origin which contains 2 vectors (0,1,1) and (1,0,-2)?



I am more interested in the method then the actual answer. Any help would be much appreciated.Maths Help. How do you find the vector equation of a plane given 2 vectors contained in the plane and a point?Let's calculate the cross product of the 2 vectors in i, j, k form:



| i j k| i j

| 0 1 1| 0 1 = -2i + j - k

| 1 0 -2| 1 0



(if you don't know how to calculate cross product I suggest you Wikipedia it.



Anyway, if your point is through the origin, then your vector equation from the plane is:



-2(x - 0) + (y - 0) - (z - 0) = 0



-2x + y - z = 0