Question
Find the vector and cartesian equation of the plane containing the two lines
and 
Solution
and 
The vector equation of the plane is
or 
The cartesian equation of plane is
or 
or (x – 2) (10 + 10) – (y – 1) (5 – 15) + (z + 3) (–2 – 6) = 0
or 20 (x – 2) + 10 (y – 1) – 8 (z + 3) = 0
or 10 (x – 2) + 5 (y – 1) – 4 (z + 3) = 0
or 10x – 20 + 5y – 5 – 4z – 12 = 0
or 10x + 5y – 4 z = 37
