I am trying to solve for the line that intersects any planes that fall under the arithmetic pattern of ax+(a+n)y+(a+2n)z=a+3n. The sample equations Ive been using is (A) x+2y+3z=3, (B) 2x-1y-4y=-7 and (C) 6x-6y-18z=-30. Using a graphing program and Gauss' elimination I know it is a line where the planes intersect rather then a point (in the final steps of the Gauss' elimination I had a bottom row of all zeros which gives unlimited answers).(adsbygoogle = window.adsbygoogle || []).push({});

I did find the cross product of vectors A and B to be -18i+18j-18k but I am not sure what to do from here to get the equation of the line. If anyone could point me in the direction or even give me a step by step of what to do or where i went wrong that would be great thanks!

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# Homework Help: The line intercept of two planes

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