Hi, I could use some help here.

a) Let u = (3, 3,1) and v = (2, 4,1) be two vectors in 3 . Determine a vector w which is orthogonal to both u and v.

b) Determine the equation of the place spanned by u and v and which goes through the origin.

c) Next, let p₁ = (6, 6, z₁ ), p₂ = (6,6, z₂ ), p₃ = (6,6, z₃ ) and p₄ = (6, 6, z₄ ) be four points in 3. Determine the four z-coordinates z_1,2,3,4 so that all four points are in the plane

I find the solution for a) that the vector w = (1, 1, 6)

But I need help with b) and c)

Thanks for helping.