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

• 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.

\$\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