# What's the point?

Geometry Level 4

The line $$\color{red}{l}$$ has equations $\dfrac{x-1}{2}=\dfrac{y-1}{3}=\dfrac{z+1}{2}$ and the point $$A$$ is $$(7, 3, 7)$$. $$M$$ is the point where the $$\color{#007fff}{\text{perpendicular}}$$ from $$A$$ meets $$\color{red}{l}$$.

The point $$\color{#ff8600}{B}$$ lies on $$AM$$ such that $$\overrightarrow { AB } =3 \, \overrightarrow { BM }$$. If the coordinates of $$\color{#ff8600}{B}$$ are $$(p, q, r)$$, find the value of $$pqr$$.

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