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Thread: 3D

  1. #1
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    3D

    $\displaystyle \textup{The distance of the point (-2,3,-4) from the line} $$\displaystyle \frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}$ $\displaystyle \textup{measured parallel to the plane}$ $\displaystyle 4x+12y-3z+1=0$ is ?
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  2. #2
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    Quote Originally Posted by banku12 View Post
    $\displaystyle \textup{The distance of the point P(-2,3,-4) from the line} $$\displaystyle \frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}$ $\displaystyle \textup{measured parallel to the plane}$ $\displaystyle 4x+12y-3z+1=0$ is ?
    1. Determine the equation of a plane E passing through P and parallel to the given plane.
    Spoiler:
    $\displaystyle \bold{E:} 4x+12y-3z-40=0$


    2.Calculate the coordinates of the point of intersection between the given line and the plane E.
    Spoiler:
    $\displaystyle \left(4,\ \frac52 ,\ 2\right)$


    3. Calculate the distance $\displaystyle d=|\overline{PE}|$
    Spoiler:
    $\displaystyle d=\frac{17}2$
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