The discussion centers on proving the coplanarity of vectors a, b, c, and d given the equation (a × b) × (c × d) = 0. Participants explore the potential application of Lagrange's identity in this proof. However, it is established that the assertion is not universally valid, as the condition (a × b) = 0 allows for arbitrary choices of vectors c and d, which do not guarantee coplanarity.
PREREQUISITESStudents and educators in mathematics, particularly those studying linear algebra and vector calculus, as well as anyone interested in the geometric properties of vectors.
It's not true.Bipolarity said:Homework Statement
If [itex](a \times b) \times (c \times d) = 0[/itex], 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 said:It's not true.
If [itex](a \times b)=0\,,[/itex] the c & d can be anything.