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If $\bar{AB} = \bar{b}$ and $\bar{AC} = \bar{c}$ then the length of the perpendicular from A to the line BC is

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$|\frac{\bar{b} × \bar{c}}{\bar{b} - \bar{c}}|$

$\frac{1}{2} |\frac{\bar{b} × \bar{c}}{\bar{b} - \bar{c}}|$

$|\frac{\bar{b} × \bar{c}}{\bar{b} + \bar{c}}|$

$2 |\frac{\bar{b} × \bar{c}}{\bar{b} - \bar{c}}|$

answer is B.

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Detailed Solution

$\frac{|\bar{AB} × \bar{BC}|}{|\bar{BC}|} = \frac{|\bar{b} × (\bar{BA} + \bar{AC})|}{|\bar{BC}|} =$

$\frac{|\bar{b} × (- \bar{b} + \bar{c})|}{|\bar{c} - \bar{b}|} = \frac{|\bar{b} × \bar{c}|}{|\bar{b} - \bar{c}|}$

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