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The plane that passes through the point $(−1,1,2)$ and contains the line of intersection of the planes $x+y−z=5$ and $2x−y+3z=1$.

Arnaldo
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T.Aung
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    what are your own thoughts? – Arnaldo Mar 23 '17 at 17:19
  • Find two points on the line and then the equation of the plane passing through three points. – egreg Mar 23 '17 at 18:28
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    Duplicate of http://math.stackexchange.com/q/137629/265466, just with different numbers. The way to go about solving the problem is exactly the same. – amd Mar 23 '17 at 22:16

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multiplying the first equation our planes by $3$ and adding to the second we have $$5x+2y=16$$ thus we get $$x=\frac{16}{5}-\frac{2}{5}$$ and from here we get $$z=\frac{9}{5}+\frac{3}{5}y$$ and the equation our line is $$[x,y,z]=[16/5;0;9/5]+t[-2/5;1;3/5]$$ can you proceed?

Dr. Sonnhard Graubner
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