Could please help me to write codes for solving the following problem:  The plane (p) includes the line (d): (x-1)/-1=y/1=(z-3)/2, and distance from it to the point M(1,0,3) equal 3. (I solved it with Maple, but the result was "no solution". Thanks so much.

With Maple, is there a way to quickly solve systems of equations where the solutions are the coordinates of a vector?
An example of an idea: A problem to solve:
There are points: M(1,0,0) and N(0,0-1); plane (Q): x-y-4=0. Determine the plane (P) containing M and N, making with (Q) a 45 degree angle.
Solution:
Assume: Equation of (P): Ax+By+Cz+D=0
We have:
Normal vector of (P): np(vector):=<A,B,C>
Normal vector of (Q): nq(vector):=<1,-1,0>
Direction vector of line NM: dNM(vector):=<1,0,1>
To determine: A, B, C, it is necessary to solve the system of equations:
cos(45 degrees)= np(vector).nq(vector)/abs(np(vector)) x abs(nq(vector))=1/Sqrt(2)
  dNM(vector).np(vector)=0....

In Maple what is the fastest way to convert a directed line segment into a vector? Please help me. Thank you a lot.

Anyone could help me know how to use of "Back Solving Assistant", please? I can't understand how to enter a formular. When I enter a formula, even the one suggested by Maple, and then click the "Proceed to Back-Solver" button, I always get an error message. Please help me!