Using magic triangle to find lengths
The diagram shows a triangle $ABC$ with $A\left( -1,2,3 \right)$, $B\left( 0,1,2 \right)$ and $C\left( 5,5,-3 \right)$.
By considering the vectors $\overrightarrow{AB}$, $\overrightarrow{CB}$ and $\overrightarrow{AC}$, and using scalar or vector product, find the exact lengths of
(a)
$AF$, where $F$ is the foot of perpendicular from $B$ to $AC$,
[2]
(b)
$AG$, where $G$ is the foot of perpendicular from $A$ to $BC$.
[2]
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