1. ## 3D

$\displaystyle \textup{The distance of the point (-2,3,-4) from the line} $$\displaystyle \frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5} \displaystyle \textup{measured parallel to the plane} \displaystyle 4x+12y-3z+1=0 is ? 2. Originally Posted by banku12 \displaystyle \textup{The distance of the point P(-2,3,-4) from the line}$$\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:
$\displaystyle d=\frac{17}2$