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MHT CET202611 April 2026Morning ShiftMathematicsVector AlgebraActual

If a, b, c are distinct non-negative numbers and the vectors a i + a j + c k , i + k , c i + c j + b k lie in the same plane, then the value of c is...

Options

  1. AThe arithmetic mean of a and b
  2. BThe geometric mean of a and b
  3. CThe harmonic mean of a and b
  4. D0

Correct answer

B. The geometric mean of a and b

Step-by-step solution

Since the given vectors are coplanar, their scalar triple product is zero. vmatrix a & a & c 1 & 0 & 1 c & c & b vmatrix = 0 Expanding the determinant along the first row: a(0 - c) - a(b - c) + c(c - 0) = 0 -ac - ab + ac + c^2 = 0 c^2 - ab = 0 c^2 = ab Since a, b, c are non-negative numbers, c = ab . Thus, c is the geometric mean of a and b . Answer: The geometric mean of a and b

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