How Far the Drone Sits Off the Wire

A straight guy-wire is anchored at the origin and runs off in the direction

$\mathbf{d} = \begin{bmatrix} 2 \\ -1 \\ 2 \end{bmatrix}$

A survey drone hovers at the point whose position vector, measured from the same anchor, is

$\mathbf{p} = \begin{bmatrix} 7 \\ 1 \\ 4 \end{bmatrix}$

All coordinates are in metres. The wire is an infinite line through the origin along $\mathbf{d}$ — the drone is not on it.

	$x$	$y$	$z$
Wire direction $\mathbf{d}$	$2$	$-1$	$2$
Drone position $\mathbf{p}$	$7$	$1$	$4$

Split $\mathbf{p}$ into the piece that lies along the wire and the piece perpendicular to it. The perpendicular piece is the drone's shortest distance to the wire.

What is that perpendicular distance, in metres? Round your answer to 2 decimal places.

How Far the Drone Sits Off the Wire

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