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Question

Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.

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Solution

We know that the equation of the plane whose intercepts on the coordianate axes are a, b and c isxa+yb+zc=1Given that the plane makes equal intercepts on the coordiante axes.So, a = b = cSo, the equation of the plane isxa+ya+za=1 x + y + z = a ... 1This plane passes through the point (2, 4, 6).Substituting this point in (1), we get2 + 4 + 6 = a a = 12Substituting this in (1), we get x + y + z = 12

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