Can Lagrange's Identity Help Prove Coplanarity of Vectors a, b, c, and d?

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The discussion centers on proving that vectors a, b, c, and d are coplanar if (a × b) × (c × d) = 0. One participant suggests using Lagrange's identity to approach the problem but expresses difficulty in starting the proof. Another contributor argues that the statement is not universally true, noting that if (a × b) = 0, then vectors c and d can be arbitrary, which undermines the coplanarity condition. The conversation highlights confusion surrounding the application of Lagrange's identity in this context. Ultimately, the participants are seeking clarity on the relationship between the vectors and the conditions for coplanarity.
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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
 
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Bipolarity said:

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.
 
SammyS said:
It's not true.

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

Thanks Sammy!

BiP
 

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