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Find the equation of the plane which passes through the point (2,-3,7) and makes equal intercepts on the coordinate axes.

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Find the equation of the plane which passes through the point (2,-3,7) and makes equal intercepts on the coordinate axes.
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Correct Answer - `x+y+z=6`
Let it make intercept a on each of the coordinate axes. Then, its equation is `x/a+y/a+z/a=1 rArr x+y+z=a`.
Putting, `x=2,y=-3,z=7`, we get `a=2+(-3)+7=6`.
So, the required equation of the plane is `x+y+z=6`.
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