Prove or disprove the following statement about vectors in :

If and , then .

This statement is false. Let , and . Then we have

but, .

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Stumbling Robot

A Fraction of a Dot
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Show that the cancellation law does not hold for the dot product

Prove or disprove the following statement about vectors in :

If and , then .

This statement is false. Let , and . Then we have

but, .