The question really is in the title. I know what it means if the dot product equals 0 but I find it interesting thinking what it means when it equals exactly 1 and can't seem to find anything online to enlighten me.
Thanks
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$\begingroup$If you already know the vectors are both normalized (of length one), then the dot product equaling one means that the vectors are pointing in the same direction (which also means they're equal).
If you already know the vectors are pointing in the same direction, then the dot product equaling one means that the vector lengths are reciprocals of each other (vector b has its length as 1 divided by a's length). For example, 2D vectors of (2, 0) and (0.5, 0) have a dot product of 2 * 0.5 + 0 * 0 which is 1. Also, (1, 1) has a length of sqrt(2), and (0.5, 0.5) has a length of 1/sqrt(2), and the dot product is also 1.
If you don't already know anything about the vectors, you can't concretely say anything about this.
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