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