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geom3d

  

distance

  

find the distance between two given objects

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

distance(A, B)

distance(l1, l2)

distance(p1, p2)

distance(A, l1)

distance(A, p1)

distance(l1, p1)

Parameters

A, B

-

points

l1, l2

-

lines

p1, p2

-

planes

Description

• 

The routine computes the distance between two given objects: points, lines, and planes, or any combination of these.

• 

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

Examples

withgeom3d:

Distance from a point to a plane

assumel0

planepp,lx+my+nz+p=0,x,y,z:

pointA,x1,y1,z1:

distanceA,pp

l~x1+my1+nz1+pl~2+m2+n2

(1)

l'l':

Find the distance from a point to a straight line

pointA,6,6,1,linel,2+t,1+2t,3t,t:

distanceA,l

12146

(2)

Find the two points on the line x=2y=3z+6 at a distance of 7 units from the plane 2x+y2z=5.

pointo,t,1t2,2+t3:

planep,2x+y2z=5,x,y,z:

ddistanceo,p:

anssolved=7,t:

foritonopsansdoanssubsopi=subst=opi,ans,coordinateso,ansend do:

coordinates of the two points are

ans

12,6,2,12011,6011,6211

(3)

See Also

assume

geom3d[sides]

geometry[distance]

Student[Precalculus][Distance]

 


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