Could you please teach me how to solve this question? I don't know how to do it at all. Thank you very much.

Question:

Prove: If a , b, c, and d lie in the same plane when positioned with a common initial point then (a*b) * (c *d) =0.

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- Jan 2nd 2007, 01:11 PM #1

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- Jan 2nd 2007, 01:19 PM #2

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$\displaystyle \bold{a} \wedge \bold{b}$ is a vector normal to the plane containg $\displaystyle \bold{a}$ and $\displaystyle \bold{b}$. Similarly $\displaystyle \bold{c} \wedge \bold{d}$ is a vector normal to the plane containg $\displaystyle \bold{c}$ and $\displaystyle \bold{d}$.

But these two planes are the same plane so $\displaystyle \bold{a} \wedge \bold{b}$ and $\displaystyle \bold{c} \wedge \bold{d}$ are parallel (or anti-parallel) and hence:

$\displaystyle (\bold{a} \wedge \bold{b}) \wedge (\bold{c} \wedge \bold{d})=0$

RonL