find the intersections between two or three given objects. - Maple Help

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geom3d[intersection] - find the intersections between two or three given objects.

Calling Sequence

intersection(obj, l1, l2)

intersection(obj, p1, p2)

intersection(obj, l1, p1)

intersection(obj, l1, s)

intersection(obj, p1, p2, p3)

Parameters

obj

-

name

l1, l2

-

lines

p1, p2, p3

-

planes

s

-

sphere

Description

• 

The routine finds the intersection between two lines, two planes, a line and a plane, a line and a sphere, or three planes.

• 

In general, the output is assigned to the first argument obj. If the routine is unable to determine the intersection(s) of given objects, it will return FAIL.

• 

If l1 and l2 are two lines, the output is either NULL, the point of intersection, or a line in case l1 and l2 are the same.

• 

If p1 and p2 are two planes, the output is either NULL, the line of intersection, or a plane in case p1 and p2 are the same.

• 

If l1 is a line and p1 a plane, the output is either NULL, the point of intersection, or a line in case l1 lies in p1.

• 

If l1 is a line and s a sphere, the output is either NULL, one point of intersections, a list of two points of intersection.

• 

If p1, p2 and p3 are three planes, the output is NULL, or the point of intersection.

• 

For more details on the output, use detail.

• 

The command with(geom3d,intersection) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

intersection of two planes

planep1,4x+4y5z=12,x,y,z:

planep2,8x+12y13z=32,x,y,z:

intersectionl,p1,p2:

detaill

Warning, assume that the parameter in the parametric equations is _t

name of the objectlform of the objectline3dequation of the linex=1+8_t,y=2+12_t,z=16_t

(1)

intersection of three planes

pointA,0,0,0,pointB,1,0,0,pointC,0,1,0,pointE,0,0,1:

planeoxy,A,B,C,planeoyz,A,C,E,planeoxz,A,B,E:

intersectionP,oxy,oyz,oxz

P

(2)

coordinatesP

0,0,0

(3)

Prove that the lines 2xy+3z+3=0=x+10y21 and 2xy=0=7x+z6 intersect. Find the coordinates of their common point, and the equation of the plane containing them.

Define the line l1: 2*x-y+3*z+3=0=x+10*y-21

planep1,2xy+3z+3=0,x,y,z:planep2,x+10y21=0,x,y,z:

linel1,p1,p2:

Define the line l2: 2xy=0=7x+z6

planep3,2xy=0,x,y,z:planep4,7x+z6=0,x,y,z:

linel2,p3,p4:

Find the intersection of l1 and l2

intersectionP,l1,l2

P

(4)

coordinatesP

1,2,1

(5)

Find the equation of the plane containing l1 and l2

planep,l1,l2:

Equationp

378+63x+189y+63z=0

(6)

Prove that the lines xaap=ybbp=zccp and xapa=ybpb=zcpc intersect, and find the coordinates of the point of intersection.

assumeap0,a0:

linel1,pointo1,a,b,c,ap,bp,cp:

linel2,pointo2,ap,bp,cp,a,b,c:

intersectionP,l1,l2

P

(7)

coordinatesP

a~+ap~,b+bp,c+cp

(8)

See Also

geom3d[line], geom3d[plane], geom3d[sphere]


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