geom3d
distance
find the distance between two given objects
Calling Sequence
Parameters
Description
Examples
distance(A, B)
distance(l1, l2)
distance(p1, p2)
distance(A, l1)
distance(A, p1)
distance(l1, p1)
A, B
-
points
l1, l2
lines
p1, p2
planes
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.
withgeom3d:
Distance from a point to a plane
assumel≠0
planepp,lx+my+nz+p=0,x,y,z:
pointA,x1,y1,z1:
distanceA,pp
l~x1+my1+nz1+pl~2+m2+n2
l≔l:
Find the distance from a point to a straight line
pointA,6,6,−1,linel,2+t,1+2t,−3−t,t:
distanceA,l
1462
Find the two points on the line x=2y=3z+6 at a distance of 7 units from the plane 2x+y−2z=5.
pointo,t,12t,−2+t3:
planep,2x+y−2z=5,x,y,z:
d≔distanceo,p:
ans≔solved=7,t:
foritonopsansdoans≔subsopi=subst=opi,ans,coordinateso,ansenddo:
coordinates of the two points are
ans
12,6,2,−12011,−6011,−6211
See Also
assume
geom3d[sides]
geometry[distance]
Student[Precalculus][Distance]
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