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AP EAMCET201922 Apr 2019Morning ShiftMathematicsVector AlgebraActual

If (P ) is a point lying on the line passing through the point (A( i - j +3 k ) ) and parallel to the vector (2 i + j -2 k ) such that (| A P |=18 ), then a position vector of (P ) is

Options

  1. A(-13 i -5 j +9 k )
  2. B(11 i +7 j -15 k )
  3. C(13 i -5 j +9 k )
  4. D(13 i +5 j -9 k )

Correct answer

D. (13 i +5 j -9 k )

Step-by-step solution

According to the given information, the diagram is shown as below. Given, ( aligned A P & =18 O A & = i - j +3 k aligned ) Now, ( A P =18 2 i + j -2 k (2)^2+(l)^2+(-2)^2 ) ( aligned & =18 2 i + j -2 k 4+1+4 & =18 2 i + j -2 k 3 & =6(2 i + j -2 k )=12 i +6 j -12 k aligned ) By triangle law, ( aligned O P & = O A + A P & = i - j +3 k +12 i +6 j -12 k & =13 i +5 j -9 k aligned )

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