## 300 Reputation

12 years, 220 days

## Normal vector of a plane...

Maple

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.`

## Equation of a sphere (4)...

Maple

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.

## Solve the system of equations...

Maple

f:=x->x^3-3*x^2+2;

g:=x->k*(x+1)+3;

solve([f(x) = g(x), diff(f(x),x) = diff(g(x),x)],[x,k]);

evalf(%);

The result of Maple is

[[x = .168254401781027, k = -.924597779530090]]

But, the system of equations has three solutions.

## Equation of a sphere (3)...

Maple

Problem. Write the equation of the sphere passing through the three points

A(-1, 2, 1), B(-3, 4, -5), C(1, 2, -3) and its centre

`1) lies in  the plane (P): 2*x + 3*y -z = 0;`
`2)lies on the sphere (x-3)^2 + (y+1/3)^2 + (z-1)^2=1.`
` `
`This is my code`
`1) `

restart;with(geom3d):

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

point(B,3,-4,5):

## Equation of a plane (9)...

Maple

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):

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