Finding the dot product.

Finding the dot item of $(-2w) \cdot w$ where $w=(0,-2,-2)$ $$\text{dot product} = \frac{v . u}{\| v \| . \| u \|}$$

So $$-2 (0,-2,-2)=(0,4,4) \\ (0+4+4) = 8 \\ (0,-2,-2)=-4 \\ 8 \times -4=-32$$

$$\| v \|= \sqrt{0^2+(-2)^2+(-2)^2}=2 \sqrt 2 \\ \|-2w \|= \sqrt{0^2+4^2+4^2}= 4 \sqrt 2\\ \frac{-32}{2 \sqrt 2 \times 4 \sqrt 2} = -64$$ Is this proper?

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2022-07-25 20:46:29
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