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JEE Main2009MathematicsVector AlgebraActual

If u , v , w are non-coplanar vectors and p, q are real numbers, then the equality [ array llll 3 u & p v & p w array ]- [ array lll p v & w & q u array ]- [ array lll 2 w & q v & q u array ]=0 holds for

Options

  1. Aexactly one value of (p, q)
  2. Bexactly two values of (p, q)
  3. Cmore than two but not all values of (p, q)
  4. Dall values of (p, q)

Correct answer

A. exactly one value of (p, q)

Step-by-step solution

aligned & (3 p^2-p q+2 q^2 ) [ array lll u & v & w array ]=0 & But [ array lll u & v & w array ] 0 & 3 p^2-p q+2 q^2=0 & 2 p^2+p^2-p q+ ( q 2 )^2+ 7 q^2 4 =0 2 p^2+ (p- q 2 )^2+ 7 4 q^2=0 aligned p=0, q=0, p= q 2 This possible only when p=0, q=0 exactly one value of (p, q)

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