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Suppose we know that (a, b) = 3 and (a, c) = 5.
Then we can deduce that (a, b + 2c) = 3 + 2 * 5 = 13.
Thus, if you know the value of (a, b) and (a, c) you can deduce
the value of the dot product of a with any vector that can
be expressed as a linear combination of b and c, that is,
as xb + yc.
The value will be x * (a, b) + y * (a, c).
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