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Let $a, b$ and $c$ be vectors in $\mathrm{R}^{3}, \times$ denotes the cross product, . the dot product. Which of the following is false?

A. $-a \times b=b \times a$

B. $(a \times b) \cdot c=a \cdot(b \times c)$

C. $a \cdot b=b \cdot a$

D. $\boldsymbol{a} \times b=\|\boldsymbol{a}\| \boldsymbol{b} \| \sin a b$

E. $\boldsymbol{a} \cdot b=\|\boldsymbol{a}\| \boldsymbol{b} \| \cos a b$
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