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

John: 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.

Answers and Views:

Answer by LithAlex
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