For three non-zero vectors `vec(a),vec(b) " and"vec(c )`, prove that `[(vec(a)-vec(b)) (vec(b)-vec(c)) (vec(c )-vec(a))]=0`

For three non-zero vectors `vec(a),vec(b) " and"vec(c )`, prove that `

1.	For three non-zero vectors `vec(a),vec(b) " and"vec(c )`, prove that `[(vec(a)-vec(b)) (vec(b)-vec(c)) (vec(c )-vec(a))]=0`
Answer» `=(veca-vecb).{(vecb-vecc)xx(vecc-veca)}` `=(veca-vecb).{vecbxxvecc-vecbxxveca-veccxxvecc+veccxxveca)}` `=(veca-vecb).{vecbxxvecc-vecbxxveca+vecxxveca}........(veccxxvecc=0)` `=(veca-vecb).{vecbxxvecc+vecaxxvecb+vecxxveca}` ` =veca.(vecbxxvecc)+veca.(vecaxxvecb)+veca.(veccxxveca)-vecb.(vecbxxvecc)-vecb.(vecaxxvecb)-vecb.(vecxxveca)` `=veca. (vecbxxvecc)+0+0-0-0-vecb.(veccxxveca)` `=veca. (vecbxxvecc)-vecb.(veccxxveca)` `=0` (STP remains same if vectors `veca,vecb,vec` are changed in cyclic order)

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For three non-zero vectors `vec(a),vec(b) " and"vec(c )`, prove that `[(vec(a)-vec(b)) (vec(b)-vec(c)) (vec(c )-vec(a))]=0`

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