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MHT CET202519 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The projection of the line segment joining the points (2,1,-3) and (-1,0,2) on the line whose direction ratios are 3,2,6 is

Options

  1. A19 7 units
  2. B17 7 units
  3. C11 7 units
  4. D15 7 units

Correct answer

A. 19 7 units

Step-by-step solution

The vector from point A(2,1,-3) to point B(-1,0,2) is computed as: AB = (-3, -1, 5) . The direction vector of the target line with ratios 3 , 2 , and 6 is d = (3, 2, 6) . Its magnitude is | d | = 7 , giving the unit vector d = 3 7 i + 2 7 j + 6 7 k . The projection of AB onto this line is determined by the dot product with the unit vector: | AB d | = | -3 3 7 + (-1) 2 7 + 5 6 7 | = | -9 -2 + 30 7 | = 19 7 . The projection is 19 7 units.

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