# 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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