Let H = Span {V 1 , V 2 } and K = Span {V 3 ,

Question:

Let H = Span {V₁, V₂} and K = Span {V₃, V₄}, where

Then H and K are subspaces of R³. In fact, H and K are planes in R³ through the origin, and they intersect in a line through 0. Find a nonzero vector w that generates that line. w can be written as c₁v₁ + c₂v₂ and also as c₃V₃ + C₄V₄. To build w, solve the equation c₁v₁ + c₂v₂ = c₃V₃ + C₄V₄ for the unknown c_j's.