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AP EAMCET202319 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let a , b , c be three non-coplanar vector. Then the point of intersection of the line joining the points a + b + c , a - b +3 c and the line joining the points 2 a - b + c , a -2 b +4 c is

Options

  1. A2 a -4 c
  2. B3 a -3 b +5 c
  3. Ca -2 b +4 c
  4. Da - b +3 c

Correct answer

C. a -2 b +4 c

Step-by-step solution

(c) Let . aligned O A & = a + b + c O B & = a - b +3 c aligned , aligned & O C =2 a - b + c & O D = a -2 b +4 c aligned Hence vector equation of line joining the points O A and O B , aligned & r = O A + ₁( O B - O A ), ₁ R & r =( a + b + c )+ ₁(-2 b +2 c ) aligned r = a (1)+ b (1-2 ₁ )+ c (1+2 ₁ ) and also vector equation of line joining the point O C and O D ...(i) aligned & r = O C + ₂( O D - O C ), ₂ R & r =(2 a - b + c )+ ₂(- a - b +3 c ) aligned r = a (2- ₂ )+ b (-1- ₂ )+ c (1+ ₂ ) ...(ii) When the two line wi

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