Proving coplanarity of vectors from (a × b) × (c × d) = 0

[Bipolarity]

Homework Statement

If $(a \times b) \times (c \times d) = 0$, show that a,b,c,d are coplanar.

Homework Equations

The Attempt at a Solution

I have done the converse of this problem, but am having trouble on how to do this. Can we perhaps use Lagrange's identity. How can I start?

BiP

 

[SammyS]

Homework Statement

If $(a \times b) \times (c \times d) = 0$, show that a,b,c,d are coplanar.

Homework Equations

The Attempt at a Solution

I have done the converse of this problem, but am having trouble on how to do this. Can we perhaps use Lagrange's identity. How can I start?

BiP

It's not true.

If $(a \times b)=0\,,$ the c & d can be anything.

 

[Bipolarity]

It's not true.

If $(a \times b)=0\,,$ the c & d can be anything.

Thanks Sammy!

BiP