Find [itex](\vec{a}\times \vec{b})\cdot \vec{c}[/itex] if [itex]\vec{a}=3\vec{m}+5\vec{n}[/itex], [itex]\vec{b}=\vec{m}-2\vec{n}[/itex], [itex]\vec{c}=2\vec{m}+7\vec{n}[/itex], [itex]|\vec{m}|=\frac{1}{2}[/itex], [itex]|\vec{n}|=3[/itex], [itex]\angle(\vec{m},\vec{n})=\frac{3\pi}{4}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

This is my approach:

[itex](\vec{a}\times\vec{b})\cdot\vec{c}=[(3\vec{m}+5\vec{n})\times(\vec{m}-2\vec{n})]\cdot(2\vec{m}+7\vec{n})=[3\vec{m}\times\vec{m}-6\vec{m}\times\vec{n}+5\vec{n}\times\vec{m}-10\vec{n}\times\vec{n}]\cdot(2\vec{m}+7\vec{n})=\bf(-11\vec{m}\times\vec{n})\cdot(2\vec{m}+7\vec{n})[/itex]

I stuck here. I don't know the coordinates of [itex]\vec{m}[/itex] and [itex]\vec{n}[/itex].

Maybe the whole approach is wrong. I don't have any other idea on solving this problem so I need your help.

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# Triple product vector problem

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