The task: Determine the plane containing point $P( -5 , 2 , 3 )$ and going through the intersection line of the planes $2x + y + 5z = 31$ and $-4x + 5y + 4z = 50$
1.: Intersect the two given planes, resulting in a line in parameter form ( $X = P + t * V$ )
2.: Determine two arbitary points on the line
3.: Form the new plane using the two points on the line and the given point P
(by creating an equation system $ax + by + cz + d = 0$, with $3$ equations with the $x$, $y$ and $z$ values of the points inserted)
- Is my approach for solving the problem right? (I don't ask for a solution!)