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AP EAMCET202317 May 2023Evening ShiftMathematicsVector AlgebraActual

Let ' O ' be the origin, A and B be two points with position vectors -3 i -3 j +4 k and 4 i -4 j -3 k respectively. Let P be a point such that the line drawn through P parallel to OB meets OA in L and another line through P parallel to OA meets OB in M . If L divides OA in the ratio 2: 3 and M divides OB in the ratio 3: 2 , then the distance from 0 to P is

Options

  1. A19 5
  2. B389 5
  3. C341 5
  4. D21 5

Correct answer

A. 19 5

Step-by-step solution

Position vector of L is 2 5 (-3 i -3 j +4 k ) Position vector of M is = 3 5 (4 i -4 j +3 k ) Since LP | and OB and PM | OA , therefore OMPL is parallelogram. aligned & O P = O L + O M =-(-6 i -6 j +8 k +12 i -12 j -9 k ) & = 1 5 (-6 i -18 j - k ) & | OP |= 1 5 36+324+1 = 19 5 aligned

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