Let A(1,-2,3), B(-1,0,1) be two points and (P): x+y+z+4=0 be a plane. Write the equation of the sphere has center lies on the line AB, radius of sphere equal to AB/6 and sphere tangent to the plane (P).

This is my code.

> restart:with(geom3d):

point(A,1,-2,3):

point(B,-1,0,1):

line(AB,[A,B],t):

eq:=Equation(AB):

point(M,op(eq)):

Let A(1,-1,-1), B(2,1,2), C(1, 3, 1) be three points and Delta: x = -t, y = -t, z = t be a line. Write the equation of the sphere (S), knowing that center of (S) lies on the line Delta, (S) passing the point A and cuts the plane passing through the  three points A, B, C cut (S) a circle has least radius.  

This is my code.

> restart;

with(geom3d):

a:=[-t,-t,t]:

Please write for me a code this problem.

Write the equation of the plane passing through the two points A(1,-2,4), B(3,5,-1) and make a least angle with the plane x + y + z + 1 = 0.

Thank you very much.

Write the equation of the line passing through the point A(2, 2, -5), parallel to the plane (P): 2x +3y -z - 17 = 0 and cut the line Delta: x = -2 +3*t, y = 4-t, z = 5 + 2*t.

1) First code.

restart:

with(geom3d):

point(A,2,2,-5):

line(Delta,[-2+3*t,4-t,5+2*t],t):

plane(P,2*x+3*y-z-17=0,[x,y,z]):

parallel(Q,A,P):

Equation(Q):

coordinates(intersection(B,Delta,Q)):

Equation(line(AB,[A,B],t));

Let A(1, 2, 3) be a point; d1: (x-2)/2 = (y+2)/(-1) = (z - 3) / 1

d2: (x--)/(-1) = (y - 1)/2 = (z  + 1) / 1.

Write the equation of the line passing through the point A, perpendicular to d1 and cut d2.

This is my code

restart;with(LinearAlgebra): with(geom3d):

A:=<1,2,3>:

B:=[2*t+2,-t-2,t+3]:

M:=<-m+1, 2*m+1,m-1>:

line(d1,B,t):

a:=convert(ParallelVector(d1),Vector):

v:=M-A: