JEE Main2003MathematicsVector AlgebraActual

If u , v and w are three non-coplanar vectors, then ( u + v - w ) .( u - v ) ( v - w ) equals

Options

A3 u . v w
B0
Cu v w
Du w v

Correct answer

C. u v w

Step-by-step solution

( u + v - w ) ( u v - u w - v v + v w )( u + v - w ) ( u v - u w + v w )= u ( u v ) 0 - u .( u w ) 0 + u .( v w )+ v ( u v ) 0 - v ( u w )+ v ( v w ) 0 - w ( u v )+ w ( u w ) 0 - w ( u w ) 0 = u ( v w )- v ( u w )- w ( u v )=[ u v w ]+[ v w u ]-[ w u v ]= u .( v w )

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