231.12.3.63 Determine the smallest distance between point and line

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In summary, the number 231.12.3.63 is a specific point on a coordinate plane that is used to find the smallest distance between a point and a given line. This refers to the shortest distance between the point and any point on the line, and is calculated using a formula that takes into account the coefficients and constant term of the line's equation. This calculation is commonly used in geometry, physics, and engineering applications to find the closest distance between two objects or points. However, there are some limitations to using this method, such as assuming a two-dimensional plane and a non-vertical line.
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karush
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$\tiny{231.12.3.63}$
$\textsf{Determine the smallest distance between point $P(1,1,1)$}$
$\textsf{ and the line $L$ through the origin}$
$\textsf{ $L$ has the direction $\langle -4,-5,8 \rangle$}$

$\textit{ok I know the formula to use basically is}$

\begin{align*}\displaystyle
d&=\frac{|Am+Bn+C|}{\sqrt{A^2+B^2}}
\end{align*}

$\textit{But did not know how to get the equation for L}$
 
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Isn't this question a duplicate of the following?

http://mathhelpboards.com/calculus-10/231-12-3-65-determine-smallest-distance-between-point-line-22060.html
 

Related to 231.12.3.63 Determine the smallest distance between point and line

1. What is the significance of 231.12.3.63 in the context of finding the smallest distance between a point and a line?

The number 231.12.3.63 is most likely referring to a specific point on a coordinate plane, such as the x, y, and z coordinates. This point is important because it is the point for which we are trying to determine the smallest distance to a given line.

2. What does the term "smallest distance" mean in this scenario?

The smallest distance between a point and a line is the shortest distance between the point and any point on the line. In other words, it is the closest distance the point can get to the line without being on the line itself.

3. How is the smallest distance between a point and a line calculated?

The smallest distance can be calculated using the formula d = |ax + by + c| / √(a² + b²), where a and b are the coefficients of the x and y terms in the equation of the line, and c is the constant term.

4. What is the purpose of determining the smallest distance between a point and a line?

This calculation is often used in geometry and physics to find the closest distance between two objects or points. It can also be used in various engineering applications, such as finding the minimum distance between a point and a potential obstruction or barrier.

5. Are there any limitations to using this method for finding the smallest distance?

Yes, this method assumes that the point and line are in a two-dimensional plane and that the line is not vertical. It also assumes that the point does not lie on the line. In certain scenarios, such as in three-dimensional space or when the point is on the line, alternative methods may need to be used.

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