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Properties of the Dot Product
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All of the following statements about the dot product of vectors in $$\mathbb{R}^2$$ are true except:

A

The dot product of two vectors is zero if and only if the vectors are perpendicular.

B

The dot product is distributive over vector addition.

C

The dot product is a commutative operation.

D

The dot product of two nonzero orthogonal vectors is equal to the product of their magnitudes.

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