The Length Nobody Measured

Two feature vectors $a$ and $b$ describe the same user in a recommender system. The individual components were discarded during a database migration — only three measured lengths survived:

Quantity	Value (units)
$\lVert a \rVert$	$5$
$\lVert b \rVert$	$7$
$\lVert a + b \rVert$	$10$

The team now needs the length of the difference vector, $\lVert a - b \rVert$ , to measure how far apart the two profiles sit.

Compute $\lVert a - b \rVert$ from the three numbers above.

Answer in units, rounded to two decimal places.

The Length Nobody Measured

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