File:Spatial vector.png

// Made with help from http://commons.wikimedia.org/wiki/Image:Wikibooks_povray_coordinates.png
#include "colors.inc"

camera {
        location <5,5,5>
        look_at  0
        right x
        up y
}

light_source {
        <5,5,5>
        color White
        shadowless
}

background {color White}

#macro Vector(Start,Length,Direction,Diameter,Color)
merge{
        cylinder {Start,Start+(Length-.29)*Direction,Diameter pigment {Color}}
        cone {(Length-.3)*Direction,Diameter*2,Start+Length*Direction,0 pigment {Color}}
}
#end

Vector (0,3,x,.05,colour <1,0,0,.9>)
Vector (0,3,y,.05,colour <0,1,0,.9>)
Vector (0,3,z,.05,colour <0,0,1,.9>)
Vector (0,1.5,x,.05001,colour <1,0,0,.7>)
Vector (0,2.5,y,.05001,colour <0,1,0,.7>)
Vector (0,2,z,.05001,colour <0,0,1,.7>)
Vector (0,1,x,.050001,colour <1,0,0,.1>)
Vector (0,1,y,.050001,colour <0,1,0,.1>)
Vector (0,1,z,.050001,colour <0,0,1,.1>)
Vector (0,vlength(1.5*x+2.5*y+2*z),(1.5*x+2.5*y+2*z)/vlength(1.5*x+2.5*y+2*z),.05,colour <1,1,1,.7>)

#macro DashedLine(Start,Length,Direction,Diameter,Color)
cylinder {Start,Start+Length*Direction,Diameter
        pigment {
                gradient Direction
                color_map {
                        [0 colour <1,1,1,1>]
                        [0.24999 colour <1,1,1,1>]
                        [0.25 Color]
                        [0.4999 Color]
                        [0.5 colour <1,1,1,1>]
                        [0.74999 colour <1,1,1,1>]
                        [0.75 Color]
                        [0.99999 Color]
                        [1 colour <1,1,1,1>]
                }
        }
}
#end

object {
        DashedLine (0,1.5,x,.05,colour <1,0,0,.7>)
        translate 2*z
}
object {
        DashedLine (0,2,y,.05,colour <0,1,0,.7>)
        translate 1.5*x+2*z
}
object {
        DashedLine (0,2,z,.05,colour <0,0,1,.7>)
        translate 1.5*x
}

#macro Label(Place,Text,Color)
text {
        ttf "crystal.ttf" Text .1, 0
        pigment { Colour }
        scale .3
        rotate <45,225,0>
        translate Place
}
#end

Label(2.85*x-.2*z,"X",colour <1,0,0,.7>)
Label(2.85*y-.2*x,"Y",colour <0,1,0,.7>)
Label(2.85*z-.2*x,"Z",colour <0,0,1,.7>)
Label(0.85*x-.2*z,"i",colour <1,0,0,.7>)
Label(0.85*y-.2*x,"j",colour <0,1,0,.7>)
Label(0.85*z-.2*x,"k",colour <0,0,1,.7>)
Label(1.35*x-z+.6*x,"rx=1.5i",colour <1,0,0,.7>)
Label(2.35*y-.2*x,"ry=2.5j",colour <0,1,0,.7>)
Label(1.85*z-.2*x,"rz=2k",colour <0,0,1,.7>)

union {
        text {
                ttf "crystal.ttf" "r=rx+ry+rz=" .1, 0
                pigment { colour <1,1,1,.7> }
                scale .3
        }
        text {
                ttf "crystal.ttf" " =1.5i+2.5j+2k=" .1, 0
                pigment { colour <1,1,1,.7> }
                scale .3
                translate -.3*y
        }
        text {
                ttf "crystal.ttf" "        |1.5|" .1, 0
                pigment { colour <1,1,1,.7> }
                scale .3
                translate -.6*y
        }
        text {
                ttf "crystal.ttf" "       =|2.5|" .1, 0
                pigment { colour <1,1,1,.7> }
                scale .3
                translate -.9*y
        }
        text {
                ttf "crystal.ttf" "        | 2 |" .1, 0
                pigment { colour <1,1,1,.7> }
                scale .3
                translate -1.2*y
        }
        rotate <45,225,0>
        translate 1.5*x+2.5*y+2*z-.2*x-.2*z
}

own work