(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let [tex]l_1:<x,y,z>=<2,-1,3>+t<-1,2,1>[/tex] and [tex]P(1,3,2)[/tex] be a line and point in R^{3}, respectively. Find the distance from P to l.

2. Relevant equations

distance between two points in R^{3}

[tex]d=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}[/tex]

and the line in this problem is given to us in vector equation form, from which I can find the directional vector v and the position vector r_{0}

3. The attempt at a solution

I'll need a bit of guidance on this problem. I believe that I'm supposed to find the shortest distance between P and some point on line L, and I can only think that the shortest distance between P and some point on L would be some path from P that intersects L at a 90 degree angle (perpendicular to L). I was thinking of perhaps using L's directional vector and the point P in order to construct some line that goes through P and is perpendicular to L, which would mean I would need to cross the directional vector with something?

I'm not too sure on how to go about this, or whether or not this is a proper way of approaching this problem.

Any guidance would be greatly appreciated.

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# Find the distance between a point and a line (given its vector equation)

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