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If vec axx vec b= vec cxx vec da n d ve...

If ` vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d ,` then show that ` vec a- vec d ,` is parallel to ` vec b- vec c`

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`{:("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.
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