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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!)
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    Yes, your approach is pretty much right. From the two points on the line and the point $P$, you can then find two vectors ("starting" at the same point) and take the cross product of those two to get a normal vector for the plane.2012-04-18
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    The procedure will work. It involves somewhat more effort than necessary.2012-04-18

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