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

1. ## (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.

2. 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