The diagram shows a triangle $ABC$ with $A\left( -1,2,3 \right)$, $B\left( 0,1,2 \right)$ and $C\lef

Question

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 $AF$, where $F$ is the foot of perpendicular from $B$ to $AC$, [2] $AG$, where $G$ is the foot of perpendicular from $A$ to $BC$. [2]

Accepted Answer

(a) $1$ unit; (b) $\frac{3\sqrt{33}}{11}$ units

Applications of Dot and Cross Product

Applications of Dot and Cross Product

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