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Find a plane containing the point (4, 4, 8) and the line of intersection of the planes 6x + 7y + 7z = 41 and - 3x - y + 7z = 0

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well, the line of intersection is

(x - 41/9) / (8/9) = y/-1 = (z - 41/21) / (5/21)

Now, do you recall how to find the plane given a point and a line?
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