Vectors and planes?

1a) find a vector that is orthogonal to the vectors (1,2,1) and (1,0,1).





1b) Use the results in part (a) to find an equation for the plane containing the two vectors (1,2,1) and (1,0,1).





I can do part A, but I'm a little confused with part B. I know that i need to use the formula a(x-x0)+b(y-y0)+c(z-z0)=0, but I don't know how to find a point. Can I just choose (1,2,1) or (1,0,1) as the point for (x,y,z)?

Vectors and planes?
In (a), you found the vector normal to the plane by taking the cross product of (1,2,1) and (1,0,1).





However, there are an infinite number of parallel planes with that normal. To determine the equation of a particular plane, you need the co-ordinates (x0, y0, z0) of a point known to lie in the plane. Then the equation


a(x-x0)+b(y-y0)+c(z-z0) = 0


will give you a unique plane.





If you don't have a point given, you can only leave the equation in terms of (x0, y0, z0).