SOLUTION: Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4). Also what point on that line is closest to the point (3,5,-4)

Algebra ->  College  -> Linear Algebra -> SOLUTION: Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4). Also what point on that line is closest to the point (3,5,-4)      Log On


   

Question 651090: Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4). Also what point on that line is closest to the point (3,5,-4)
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Sorry, I clicked "post" before I finished.  Come back later. and I'll
finish it


Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4).
The distance between a point Q and a line in space is given by the formula
           ‖PQ×u‖
      D =  ------ 
            ‖u‖

where u is the direction vector for the line and P is a point on the line.

First we find PQ×u where Q(3,5,-4) and we'll
take P(5,2,7) and 

PQ×u = < 5-3,2-5,7-(-4) > = < 2,-3,11 > 

Next we use the points (5,2,7) and (-3,6,4) to find a direction vector u for the line.

u = < -3-5,6-2,4-7 > = < -8,4,-3 >



edwin