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Mathematics-Online problems:

Interactive Problem 174: Distance Point-Plane, Line-line, Construction of a Plane

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
#./interaufg174_en.tex#In $ \mathbb{R}^3$ let $ g_1$ and $ g_2$ be the lines given by the parametric equations

$\displaystyle g_1: \vec{x}=\left(\begin{array}{c}4\\ 0\\ 3\end{array}\right)+s\... ...\ 2\\ -1\end{array}\right)+t\left(\begin{array}{r}0\\ 2\\ -1\end{array}\right) $

and let $ E_1$ be the plane with the equation

$ E_1: x_1-4x_2+8x_3=3$.

a)
Compute the distance of $ E_1$ from the origin.
b)
Compute the distance between both lines.
c)
Determine the plane $ E_2$ which is parallel to $ g_1$ and $ g_2$ and which has the to both lines the same distance.

Solution:

a)
b)
$ d^2=$
c)
$ x_1+$$ x_2+$$ x_3=1$
(rounded to four digits after the decimal point.)


   

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see also:

[Solutions]
  automatically generated: 2/ 6/2018