Product of two magnitude of vectors

[songoku]

Homework Statement

Let A, B, C and D are 4 points in 3 dimensional space. If |AB| = 3, |BC| = 7, |CD| = 11 and |DA| = 9, calculate |AC| . |BD|

Relevant Equations

magnitude of vector

dot product

I don't really know where to start. Trying to use cosine rule but failed because no information about angle.
Thanks

 

[haruspex]

Your question as stated does not involve a dot product. Did you mean $|\vec{AC}.\vec{BD}|$?
Also, as stated, it clearly is unsolvable. You could easily vary |AC| while keeping |BD| fixed. Not sure yet if changing it to the dot product of the vectors resolves that.

 

[songoku]

Your question as stated does not involve a dot product. Did you mean $|\vec{AC}.\vec{BD}|$?

No, the question really states: $|\vec{AC}| .| \vec{BD}|$ so I interpret it as product of magnitude of vector AC and BD

Also, as stated, it clearly is unsolvable. You could easily vary |AC| while keeping |BD| fixed. Not sure yet if changing it to the dot product of the vectors resolves that.

Oh ok, I see your point.

Thank you very much haruspex