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JEE Main202622 January 2026Morning ShiftMathematicsVector AlgebraActual

Let AB =2 i +4 j -5 k and AD = i +2 j + k , R . Let the projection of the vector v = i + j + k on the diagonal AC of the parallelogram ABCD be of length one unit. If , , where > , be the roots of the equation ² x²-6 x+5=0 , then 2 - is equal to

Options

  1. A3
  2. B4
  3. C1
  4. D6

Correct answer

A. 3

Step-by-step solution

AC = AB + AD = 3 i + 6 j + ( -5) k . Projection of v = i + j + k on AC : | v AC | | AC | = 1 . v AC = 3+6+( -5) = +4 , | AC | = 45+( -5)^2 . ( +4)^2 = 45 + ( -5)^2 8 +16 = 45-10 +25 18 = 54 = 3 . Equation: 9x^2 - 18x + 5 = 0 (3x-1)(3x-5) = 0 x = 1 3 , 5 3 . = 5 3 , = 1 3 . 2 - = 10 3 - 1 3 = 3 .

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