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__P__in R^3 and a 2-dimensional linear subspace S (a plane) which consists of all elements of R^3 orthogonal to

__P__.

The point

__P__itself is element of S.

So I can write

__P__' (

__x__-

__P__) = 0

to characterize all such points

__x__in R^3 orthogonal to

__P__.

__P__' means the transpose of

__P__.

My problem is to find a basis of S. This basis should depend on point

__P__.

I tried to find such a basis (alpha,beta) using the parameter form of the plane

__x__=

__P__+ alpha

__u__+ beta

__v__

but I am unable to find two vectors

__u__and

__v__orthogonal to

__P__.

I expect that this problem should be easy but I am nevertheless unable to solve it

__:(__

Please help me a bit.