Skew Lines

Author

Eric W. Weisstein
November 23, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SolidGeometry/SkewLines.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SkewLines.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Requirement for skew lines

(d1=Append[Array[#,4]&/@{x,y,z},Table[1,{4}]])/.v_[i_]:>Subscript[v,i]//MatrixForm//TraditionalForm

(d2=(v[3]-v[1]).Cross[v[2]-v[1],v[4]-v[3]])/.v[i_]:>Subscript[StyleForm[x,FontWeight->"Bold"],i]//TraditionalForm

vec[i_]:={x[i],y[i],z[i]}

Simplify[Det[d1]-d2/.v->vec]

The lines are skew if d≠0

Example

<<Graphics`Colors`;
<<LiveGraphics3D`;

WriteLiveForm["skewline.m",Show[Graphics3D[{
Thickness[.02],
{Blue,Line[{{-.1,0,0},{.9,0,0}}]},
{Red,Line[{{0,.75,-.5+.1},{.4,-.5,.5+.2}}]}
},
AspectRatio->Automatic],
ViewPoint->{1.1,-2.4,1.8}]]