5 scalar products

Geometry Level 5

Let \(\overrightarrow{k}, \overrightarrow{l}, \overrightarrow{m}, \overrightarrow{n}\) are four distinct unit vectors in space such that: \[\overrightarrow{k}.\overrightarrow{l}=\overrightarrow{l}.\overrightarrow{m}=\overrightarrow{m}.\overrightarrow{k}=\overrightarrow{n}.\overrightarrow{l}=\overrightarrow{n}.\overrightarrow{m}=-\dfrac{1}{11}\]

The value of \(\overrightarrow{k}.\overrightarrow{n}\) can be express as \(-\dfrac{A}{B}\), where \(A, B\) are coprime positive integer.

Find the value of \(A+B\).

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