Calculating Distance Between Point and Line in 3-Dimensional Space

  • Thread starter infinitylord
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    Optimization
In summary, the conversation discusses the calculation of the distance between a point and a line in three-dimensional space. The person mentions their self-taught knowledge of calculus and their attempt to solve the problem using slope and distance formulas. However, they realize that it may not be possible and seek help. They are advised to consider constructing a perpendicular line passing through the given point instead, and to use Google to find resources on how to do so.
  • #1
infinitylord
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I am completely self taught in Calculus, but I would like to have a better understanding of it before I go to College. I was looking up problems and came across this:
What is the distance d between the point A(2,-6,1) and the line l through B(3,4,-2) and C(7,-1,5)?

I attempted this by finding 3 slope formulas of the line between B and C in terms of alternating variables. (I already know this can't quite work, as the final formula will have multiple variables with no chance for substitution or elimination ). But nevertheless, I continued by creating a distance formula plugging in the slopes I got earlier for the x, y, and z variables. Remembering how to do optimization in single variable calculus, I took the derivative of the formula. I actually used a dell operator and set the numerator equal to zero. But this is definitely impossible. So now I need someone to help me out with this! Thanks!
 
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  • #2
Think instead about constructing a line passing thru point A which is perpendicular to the line passing thru B and C. Not every problem requires calculus to provide a solution.
 
  • #3
I understand what you mean. But how exactly do I do that?
 
  • #4
Google is your friend.
 
  • #5
Unfortunately I tried to look it up before I posted on here. The Google skills are lacking with me. What Should I look up? Linear Algebra or vector calculus or something?
 
  • #6
Google "distance from point to line"
 

What is 3-Dimensional Optimization?

3-Dimensional Optimization is a mathematical technique used to find the maximum or minimum values of a function with three independent variables. It involves finding the optimal combination of these variables to achieve the desired outcome.

How is 3-Dimensional Optimization different from 2-Dimensional Optimization?

In 3-Dimensional Optimization, there are three independent variables involved, whereas 2-Dimensional Optimization only has two. This means that there are more possible combinations of variables to consider, making the optimization process more complex.

What are some real-world applications of 3-Dimensional Optimization?

3-Dimensional Optimization is commonly used in fields such as engineering, economics, and physics to optimize the design of structures, maximize profits, and find the most efficient solutions to physical problems.

What is the process for performing 3-Dimensional Optimization?

The process for 3-Dimensional Optimization involves defining the objective function, which represents the desired outcome, identifying the constraints that limit the possible values of the variables, and then using mathematical techniques, such as gradient descent or simplex method, to find the optimal values for the variables.

What are some challenges of 3-Dimensional Optimization?

One of the main challenges of 3-Dimensional Optimization is the increased complexity compared to 2-Dimensional Optimization, which can make it more difficult to find the optimal solution. Additionally, the accuracy of the results can be affected by the accuracy of the initial assumptions and the limitations of the mathematical techniques used.

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