]> Example
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## Example

Suppose we know that $( a ⟶ , b ⟶ ) = 3$ and $( a ⟶ , c ⟶ ) = 5$ .

Then we can deduce that $( a ⟶ , b ⟶ + 2 c ⟶ ) = 3 + 2 * 5 = 13$ .

Similarly, 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 $x b ⟶ + y c ⟶$ .

The value will be $x * ( a ⟶ , b ⟶ ) + y * ( a ⟶ , c ⟶ )$ .

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