Finding the shortest distance from a point to a line with parametric vector equation?

"Find the shortest distance from the point P = P(-1,0,2) to the line given by the parametric vector equation

**r** = **j** - 2**k** + t(**i** + **j** + 3**k**)."

I have no clue with how to answer this question. I have considered on whether you would change the parametric vector equation into a Cartesian equation and somehow incorporate the point to find the distance from there although, it does sound a bit confusing to me. Moreover, how are you able to find the shortest distance? - As in, is there a particular approach to follow that allows you find the shortest distance from a point? It's something that I have not really come across in my course notes, lectures or textbook.

Re: Finding the shortest distance from a point to a line with parametric vector equat

the answer is (1078)^(1/2)/11

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Re: Finding the shortest distance from a point to a line with parametric vector equat

Hi,

In several responses to this problem, a formula for the distance is indicated. I think the formula is complicated and not worth memorizing, but the derivation is so simple that you can recover the formula almost immediately. Here it is:

Attachment 28087