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Does anyone has answer for the following doc product problem?

Let A,B,C be three vectors of magnitude of 1.

Let A*B = Cos(x) ( * means dot product) B*C = Cos(y) A*C = Cos(z)

For 2 or 3 dimensional space, we have z <= x + y.

My question is, can we extend this inequality to N-dimensional space?

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1 Answer 1

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Any three vectors, like your $A,B,C$, in an $N$-dimensional space lie in a $3$-dimensional subspace. So the general result follows from the $3$-dimensional one.

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