Suppose u, v V and ||u|| = ||v|| = 1 with < u,v > = 1: Prove that u = v.
Any two or more vectors will be equal if they are collinear, codirected, and have the same magnitude.
Given
and are collinear, codirected.
The unit vectors and have the same magnitude, are collinear, codirected.
Therefore the vectors and are equal.
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