Let L1 be the line passing through the point P1=(9, −1, 15) with direction vector →d1=[−2, −1, −3]T, and let L2 be the line passing through the point P2=(9, 4, 8) with direction vector →d2=[−2, −1, −1]T.

Question

Let L1 be the line passing through the point P1=(9, −1, 15) with direction vector →d1=[−2, −1, −3]T, and let L2 be the line passing through the point P2=(9, 4, 8) with direction vector →d2=[−2, −1, −1]T.
Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1, Q2) = d. Use the square root symbol '√' where needed to give an exact value for your answer. 
I have found the distance by using the formula "distance = projection of the P1P2 vector onto N. N is the cross product of the direction vectors." "(PQ-> dotted N)/|N|" I tried to make that formula make as much sense as I could. The value I got for distance is 10/Sqrt(5). What I don't know how to do is find the Q1 and Q2 values that satisfy the equation above. Any help is appreciated.

Worm · Answer

no