The coordinates of points $A$, $B$ and $C$ are $(-2,5,0)$, $(0,-2,6)$ and $(1,0,-2)$. Fi

Question

The coordinates of points $A$, $B$ and $C$ are $(-2,5,0)$, $(0,-2,6)$ and $(1,0,-2)$. Find the length of projection of $\overrightarrow{AB}$ on $\overrightarrow{AC}$. Hence, find the shortest distance of point $B$ to line $AC$.

Accepted Answer

Projection length $=\frac{29}{\sqrt{38}}\text{ units}$. Shortest distance from $B$ to line $AC$ $=\sqrt{\frac{2541}{38}}\approx8.18\text{ units}$ (3 s.f.).

Vectors - Projection Lengths

Vectors - Projection Lengths

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