@rlopez 

Can you tell more clearly how to set the distance to 0? As I understand, distance(L1,L2) is a command to find the distance between 2 given lines. I don't know how to use it when the distance is known and the equations of the lines are unknown

@rlopez

There are different routes to Rome! It's interesting! 

@Kitonum

May I ask? Why is the assigned value of the variable t (=3), from the result of the sol command, not used in the last statement? 

@vv 

The solution is really great! Fast and compact. Unfortunately I have no almost knowledge of linear algebra (vectors, matrices, ...). In my country, linear algebra is only taught at university level to students majoring in engineering, while I am a medical doctor myself.

@rlopez

Thank you a lot for your help! 

@Kitonum 

Thank you very much for your kind help!

@Rouben Rostamian  

Thank you very much for your help!  Maple is a great math software, but for me, a novice, it is difficult to use.

@vv 

Thank you so much for your help!

@Rouben Rostamian  

Let A and B be the intersection of d with d1, and d2 respectively. The coordinates of A (xa,ya,za), B(xb,yb,zb) are the solutions of the system of equations describing the line d with the equations of d1 and d2. Since M, A and B are in line, (xa-xm)= k(xb-xm), (ya-ym)=k(yb-ym),(za-zm)=k(zb-zm). Solve the system of equations to determine the solutions t1, t2 and k. Then determine the equation of d.

@Kitonum 

Thanks very much! If you don't mind, can you help me write commands to solve this problem in the direction of finding the coordinates of the point M', which is the projection of M onto the plane (P), where M' is the solution of the system of equations in the center of the plane. The sphere has center M, radius = 1/4 and plane (P). As a newbie to Maple I'm having a hard time writing commands.

@Kitonum 

I am still confused in solving the problem. Suppose the conditions are satisfied, for example, the distance between point M to the plane (P) is now =1/4 (less than the distance to the line d, please help me solve it with the commands by Maple Thank you very much!

@Kitonum 

Wow! How did I solve it?! The two equations are defined as: 5x+3y+z-8=0 and 3x+5y-z=0. Maybe I'm making a mistake again (?!) I'll check again.

@Kitonum

Sorry, I was wrong again. The coordinates of point M are exactly (1,0,2). 

@Kitonum 

I didn't check the alignment of point M with line d, just trying to find the solution! My error!. Thank you so much.

@tomleslie 

Thank you very much. Maple asked me to email the development team to describe the bugs. You did it for me and many other users.