Let a and b be two vectors such that | a|=1, | b|=4, and a b=2.

Question

Let $\vec a$ and $\vec b$ be two vectors such that $|\vec a|=1$, $|\vec b|=4$, and $\vec a\cdot\vec b=2$. If $\vec c=2(\vec a	imes\vec b)-3\vec b$, then $\vec b\cdot\vec c$ is:

Accepted Answer

$$\vec b\cdot\vec c = \vec b\cdot\big(2(\vec a\times\vec b)-3\vec b\big) = 0-3|\vec b|^2 = -3(16) = -48$$

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