1. ## Plane (geometry)

The question goes like this-
Find the equation of the plane containing the lines through the origin with direction cosines proportional to 2,1,-2 and 5,2,-3.
I have done most of the part,but got confused on this part-
I got two equations
5a+2b-3c=0
2a+b-2c=0
I just don't know how to apply cross multiplication for a,b and c.

2. $\left| {\begin{array}{rrr} i & j & k \\ 5 & 2 & { - 3} \\
2 & 1 & { - 2} \\ \end{array} } \right| = i\left| {\begin{array}{rr}
2 & { - 3} \\ 1 & { - 3} \\ \end{array} } \right| - j\left| {\begin{array}{rr} 5 & { - 3} \\ 2 & { - 2} \\ \end{array} } \right| + k\left| {\begin{array}{rr} 5 & 2 \\ 2 & 1 \\ \end{array} } \right|$

Now can you finish?