# (a*b) * (c *d) =0

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• Jan 2nd 2007, 01:11 PM
Jenny20
(a*b) * (c *d) =0
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.
• Jan 2nd 2007, 01:19 PM
CaptainBlack
Quote:

Originally Posted by Jenny20
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.

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

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

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

RonL