Question 651090
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Sorry, I clicked "post" before I finished.  Come back later. and I'll
finish it
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Find the distance from the point (3,5,-4) to the line that passes through the points (5,2,7) and (-3,6,4).
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The distance between a point Q and a line in space is given by the formula
           &#8214;<span style="text-decoration: overline">PQ</span>×<span style="text-decoration: overline">u</span>&#8214;
      D =  ------ 
            &#8214;<span style="text-decoration: overline">u</span>&#8214;

where <span style="text-decoration: overline">u</span> is the direction vector for the line and P is a point on the line.

First we find <span style="text-decoration: overline">PQ</span>×<span style="text-decoration: overline">u</span> where Q(3,5,-4) and we'll
take P(5,2,7) and 

<span style="text-decoration: overline">PQ</span>×<span style="text-decoration: overline">u</span> = < 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 <span style="text-decoration: overline">u</span> for the line.

<span style="text-decoration: overline">u</span> = < -3-5,6-2,4-7 > = < -8,4,-3 >



edwin</pre>