Items tagged with geom3d geom3d Tagged Items Feed

I have a list L. In geom3d, I want to write all tangent of plane of the sphere S from L. But I don't know. I only write one point . I tried 

> restart:

with(geom3d):

L:=[[-5, -5, 8], [-5, -1, 10], [-5, 3, 10], [-5, 7, 8], [-5, 8, -5], [-5, 8, 7], [-5, 10, -1], [-5, 10, 3], [-1, -5, 10], [-1, 7, 10], [-1, 10, -5], [-1, 10, 7...

In geom3d, how can i make a triangle which coordinates of the center circle circumscribed triangle are integer numbers? Please help me. Thank you.

I want to write the equation of the plane which equidistant the two the planes P and Q. This is my code

restart:

with(geom3d):

plane(P,2*x+3*y-6*z+1=0,[x,y,z]):

plane(Q,x -4*y-8*z+1=0,[x,y,z]):

point(M,x,y,z):

E:=distance(M,P)- distance(M,Q);

simplify(%);

but, i can simplify(E). Please help me.

In geom3d, i have equation a plane. Now i want to get two points A and B in the plane P and write the equation of the line which passing two point A, B. 

restart:
with(geom3d):
plane(P, 2*x + 2*y -z + 4=0,[x,y,z]):

f := (a,b,c) -> eval(lhs(Equation(P)), [x=a,y=b,z=c]): 

T:=f(-1,2, a):
eq:=solve(T=0,a): coordinates(point(A,-1,2,eq)):

In geom3d, how i can subs coordinates of a point M(t+1, t - 2, t+ 3) into equation of a plane (P) has equation x + 2*y -3*z + 1 = 0? Please help me.

Problem. In the plane 2*x -3*y +3*z -17 = 0, find a point M such that the sum of its distances from the poits A(3, -4, 7) and B(-5, -14, 17) will have the least value.

First way.

restart:with(geom3d):

point(A,3,-4,7):

point(B,-5,-14,17):

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

reflection(Q,A,P):

line(BQ,[B,Q]):

Problem. write the equation of the line cut the two lines d1: x = 2*t, y= -t+1, z = t-2, d2: x = -1+2*m, y = 1+m, z = 3 and perpendicular to the plane 7*x+y-4*z=0. 

This is my code. 

> restart;with(geom3d):

with(LinearAlgebra):

a:=[2*t,-t+1,t-2]:

b:=[-1+2*m,1+m,3]:

line(d1,a,t):

line(d2,b,m):

With(geom3d), equation of  a line has the form a parametric equation. How  i can get canonical equation of a line? Please help me?

I want to put vector n = (a, b, c) as normal vector of plane with assume a^2 + b^2 + c^2 > 0. For example

with(geom3d):assume(a^2 + b^2 + c^2>0):

plane(P,a*(x-1) + b*(y+2) + c*(z-3)=0,[x,y,z]);

But, i got: "Error, (in geom3d:-plane) unable to define the plane"

Plese help me. How can i put vector n = (a, b, c) as normal vector of plane?

Thank you very much.

Write the equation of the sphere has its centre at C(1, 2, 3) and cut the  straight line

Delta: x = t+1, y = t-1, z = -t at the points A and B so that the triangle ABC is a equilateral triangle.

This is my code.

Problem. Write the equation of the tangent planes to the sphere

x^2+  y^2 + z^2 -10*x +2*y +26*z -113=0

which are parallel to the lines

d1: x = -5+2*t, y = -3*t+1, z = -13+2*t

d2: x = -7+3*t, y = -1-2*t, z = 8.

This is my code

restart:

with(geom3d):

line(d1,[-5+2*t,-3*t+1,-13+2*t],t):

a:=ParallelVector(d1):

line(d2,[-7+3*t,-1-2*t,8],t):

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]:

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));

Problem. Write the equation of the plane passing the point H(1,1,1) and cut the coordinates axes Ox, Oy, Oz at A, B, C respectively so that H is centre of the circumscribed of the trianlge ABC.

This is my code.

restart:

with(geom3d):

with(LinearAlgebra):

A:=:

B:=:

C:=:

H:=:

f:=(x,y,z)->x/a + y/b +z/c-1:

solve([f(H[1],H[2],H[3]) = 0, Norm(H - A, 2) = Norm(H - B, 2), Norm(H - A, 2) = Norm(H - C, 2)],{a,b,c}): assign(%):

Problem. Write the equation of the plane passing the point H(2, 1, 1) and cuts the coordinates Ox, oy, oz at A, B, C respectively so that H is orthocenter of the triangle.

This is my code.

restart:

with(geom3d):

with(LinearAlgebra):

A:= <a,0,0>:

B:=<0,b,0>:

C:=<0,0,c>:

H:=<2,1,1>:

f:=(x,y,z)->x/a + y/b +z/c-1:

eq:=solve([f(H[1],H[2],H[3]) = 0,DotProduct(B-C, A-H, conjugate = false...