Spatial vector

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

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

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

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

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

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