Finding the equations of two intersecting planes when the symmetric equation of the intersecting line is given.

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The symmetric equation of the line at the intersection of the two planes given is:

$(x-xo)/a = (y-yo)/b = (z-zo)/c $

From this all I could get is that point $(xo, yo, zo)$ lies on the line which has the direction $(a,b,c)$. To find the equation of the two planes I need to find the normals of the respective planes for which the given info acc. to me isn’t enough.Any detailed soln. will be much appreciated

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While, in $3$ dimensional space, almost all pairs of planes determine a unique line which is their intersection (the exception is for pairs of parallel planes), the opposite is not true, if by opposite one means that every line should determine a unique pair of planes of which it is the intersection. Indeed, the correspondence between pairs of non-parallel planes on one hand and lines given by intersection on the other is many-to-one; in posh language it defines a map from pairs of non-parallel planes to lines that is not injective (though it is surjective, but that is another matter entirely).

In short, there is no hope that you can find a unique solution to your problem, though in every instance you can easily find some pair of planes that will do. Finding a single formula that will pick one solution for you in general case may not be easy, or even possible (depending on what exactly you understand by a formula).