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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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