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MHT CET202415 May 2024Morning ShiftMathematicsVector AlgebraActual

If u , v and w are three non-coplanar vectors, then ( u + v - w ) [( u - v ) ( v - w )] is equal to

Options

  1. Au ( v w )
  2. Bu ( w v )
  3. C3 u ( v w )
  4. D0

Correct answer

A. u ( v w )

Step-by-step solution

aligned & aligned ( & u + v - w ) [( u - v ) ( v - w )] = & u ( u v )- u ( u w )+ u ( v w )+ v ( u v ) & - v ( u w )+ v ( v w )- w ( u v ) & + w ( u w )- w ( v w ) = & [ u v w ]-[ v u w ]-[ w u v ] aligned & =[ u v w ]+[ u v w ]-[ u v w ] & = & = u ( v w_w ) aligned

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