intersection of two subsets of vectors and its geometrical meaning E and F is a subset of $ \mathbb R^3$. 
How to compute $ P = E \cap F $ ? 
What is the geometrical meaning of E, F and P ?
$  E =\left( \begin{array}{ccc}
1  \\
2  \\
-3  \end{array} \right)+\alpha\left( \begin{array}{ccc}
1  \\
0  \\
1  \end{array} \right)+\beta  \left( \begin{array}{ccc}
1  \\
1  \\
1  \end{array} \right)  $
$  F =\left( \begin{array}{ccc}
-2  \\
1  \\
4  \end{array} \right)+\gamma\left( \begin{array}{ccc}
0  \\
1  \\
1  \end{array} \right)+\delta  \left( \begin{array}{ccc}
-1  \\
3  \\
2  \end{array} \right)  $

To find the intersection, the analytic way would be to write out both planes as equations of the form $ax + by + cz + d = 0$, equate the left hand sides of each plane's equations with each other, and solve for x, y, and z.
