3 Intersecting Planes

Geometry Level pending

Find the sum of the coordinates of the common point of planes \(\Pi _{1}\) (which is formed from line \(l\) and point \(A\)), \(\Pi _{2}\) and \(\Pi _{3}\).

\(l:\frac{x-2}{5}=\frac{4-y}{2}=-3-z\)

\(A:\begin{pmatrix} 8\\ 2\\ 1 \end{pmatrix}\)

\(\Pi _{2}:-3x+20y-15z=1\)

\(\Pi _{3}:3x+y-z=9\)

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