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JEE Main2005MathematicsThree Dimensional GeometryActual

Let a, b and c be distinct non-negative numbers. If the vectors a i +a j +c k , i + k and c i +c j +b k lie in a plane, then c is

Options

  1. Athe Geometric Mean of a and b
  2. Bthe Arithmetic Mean of a and b
  3. Cequal to zero
  4. Dthe Harmonic Mean of a and b

Correct answer

A. the Geometric Mean of a and b

Step-by-step solution

Vector a i +a j +c k , i + k and c i +c j +b k are coplanar aligned & | array lll a & a & c 1 & 0 & 1 c & c & b array |=0 c^2=a b & a, b, c are in G.P. aligned

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