If `vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd` show that `(veca-vecd)` is parallel to `(vecb-vecc). It is given that `vec!=vecd and vecb!=vecc.

Explanation

`{:("we have ",vecaxxvecb=veccxxvecd),(and,vecaxxvecc=vecbxxvecd):}]`
`veca-vecd "will be parallel to" vecb-vecc`
`if (veca-vecd)xx(vecb-vecc)=vec0`
` if(veca-vecd)xx(vecb-vecc)=vec0`
`i.e. if vecaxxvecb-vecaxxvecc-vecd xxvecb+vecd xxvecc=vec0`
`if (vecaxxvecb+vecd xx vecc)-(vecaxxvecc+vecd xxvecb)=vec0`
`if (veca xx vecb-veccxxvecd)-(vecaxxvecc-vecb xxvecd)=vec0`
`if vec0-vec0=vec0`
`vec0=vec0` which is ture
Hence the result.