test if two objects are perpendicular to each other - Maple Help

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geom3d[ArePerpendicular] - test if two objects are perpendicular to each other

Calling Sequence

ArePerpendicular(dseg1, dseg2, cond)

ArePerpendicular(l1, l2, cond)

ArePerpendicular(l1, p1, cond)

ArePerpendicular(p1, p2, cond)

ArePerpendicular(s1, s2, cond)

Parameters

dseg1, dseg2

-

directed line segments

l1, l2

-

lines

p1, p2

-

planes

s1, s2

-

spheres

cond

-

(optional) name

Description

• 

The routine returns true if the given objects are perpendicular to each other; false if they are not; and FAIL if it is unable to reach a conclusion.

• 

In case of FAIL, if the third optional argument is given, the condition that makes the given objects perpendicular to each other is assigned to this argument.

• 

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

Examples

withgeom3d:

Show that the following spheres are mutually orthogonal:

assumea,real,a0:

spheres1,x2+y2+z2=a2,x,y,z:

spheres2,x2+y2+z22ay2az+a2=0,x,y,z:

spheres3,x2+y2+z22ax2az+a2=0,x,y,z:

spheres4,x2+y2+z22ax2ay+a2=0,x,y,z:

forito3doforjfromi+1to4doifArePerpendiculars||i,s||jthenprinti,j,trueelseprinti,j,falseend ifend doend do

1,2,true

1,3,true

1,4,true

2,3,true

2,4,true

3,4,true

(1)

See Also

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


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