Help do this simple simple question

[rock.freak667]

Homework Statement

Find the perpendicular distance from the point with coordinates $$(1,3,2)$$ to the line whose equation is $$\frac{x-2}{3}=\frac{y-8}{4}=\frac{z+1}{-1}$$

Homework Equations

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The Attempt at a Solution

Well can someone just tell me the basic outline of this question? From what i can gather to find the distance is to find the distance from the plane given to that point right?

 

[EnumaElish]

At a perpendicular angle. I think that means "the minimum distance."

 

[Dick]

it's not a plane, it's a line. How are you being taught to do these? EnumaElish is suggesting you minimize the function (x-1)^2+(y-3)^2+(z-2)^2 subject to the constraints of the line (which will let you eliminate all but one variable). You could also do it in a vector style by considering the line as a point plus direction vector. Which sounds more familiar?

 

[HallsofIvy]

There are many different ways to do a problem like this. There are, in fact, formulas exactly for a situation like this where you can just plug the numbers into the formula. The problem with not showing any work at all is that we have no idea which would be appropriate for you. Surely you have not been given a problem like this with no instruction at all. What do you know and what do you have to work with for problems like this.

 

[rock.freak667]

Well the only vector things I have learned about an equation like that is
if $$\frac{x-2}{3}=\frac{y-8}{4}=\frac{z+1}{-1}$$

then the plane passes through the point $$(2,8,-1)$$ and direction is$$\begin{array}{c}<br /> 3 \\<br /> 4 \\<br /> { - 1} \\<br /> \end{array}$$

 

[Dick]

Then consider the vector from (2,8,-1) to (1,3,2). You want to split that up into components that are parallel and perpendicular to the direction vector of the line. Remember dot products? Then find the length of the perpendicular component.