Problem. Write the equation of the line Delta which parallel to the planes 

(P): 3x +12y -3z -5 = 0, (Q): 3x -4y +9z + 7 = 0

and cuts two the lines

(d1): x = 2t -5, y = -4t + 3, z = 3t -1

(d2): x = -2m + 3,  y = 3m  - 1, z = 4m + 2.

This is my idea.

1) Put A(2t -5, -4t + 3, 3t -1) and B(-2m + 3, 3m  - 1, 4m + 2).

2) Find coordinates of vector AB.

3) Because Delta parallel to the planes (P...

Problem: Let (d): x = 2*t + 3, y = t -2, z = -t -1 be a line and (P): x+ y + z + 2 = 0 be a plane. Write the equation of a line Delta lies in the plane (P), Delta perpendicular to the line (d

Let A(2;-2;3), B(4;-5;6) and (M(1;2;3) be three points. Write the equation of the plane (P) passing through two points A and B 

Problem: Write the equation internal bisector and external bisector of a triangle ABC with A(1,2,-7), B(3,-1,-1), C(-5,14,-3). This is my code.

restart;
> with(LinearAlgebra):
> A:=: B:=: C:=: M:=:

>v:=1/Norm(A-B,2)*(A - B) + 1/Norm(A-C,2)*(A - C): M=A + v*t;

>u:= 1/Norm(A-B,2)*(A - B) - 1/Norm(A-C,2)*(A - C): M=A + u*t;

in the commands M = A + v*t and M = A + u*t, please comment for me. Thank you.

Please help me  write a code for the following problem:

Write the equation of the plane which passes through the points A(-1, 3, -6) and B(2, 2, -10) and tangent to the sphere

(x-1)^2 + (y + 1)^2 + (z - 7)^2 = 9.

Thank you very much.