Find the length and equations of the line of shortest distance between the lines given by: (x-8)/3=(y+9)/(-16)=(z-10)/7 and (x-15)/3=(y-29)/8=(z-5)/(-5) The answer given in the book is:14 units, (x-5)/2=(y-7)/3=(z-3)/6 NOTE: Thank you very much for answering my question posted on 18 May,2013. I also solved this question, but the answer did not come to ?/2 and therefore I posted this question. Please note that there is no mistake in typing at all. A couple of questions or answers to them are wrong in every exercise relating to 3D Geometry.

let P and Q be the points on the given lines, respectively. then the general coordinates of P and Q are:

therefore the direction ratios of PQ are 

now PQ will be the shortest distance if it is perpendicular to both the given lines, therefore by the condition of perpendicularity,

now solving (1) and (2),

equation (1) becomes: 

equation (2) becomes: 

now solving 1(a) and 1(b), we get

hence the points are

therefore the shortest distance between the lines

since we have the points P and Q, the equation of the line which passes through two given points is: