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AP EAMCET201823 Apr 2018Morning ShiftMathematicsVector AlgebraActual

If a , b , c are non coplanar vectors, then the point of intersection of the line passing through the points 2 a +3 b - c , 3 a +4 b -2 c with the line joining the points a -2 b +3 c , a -6 b +6 c is

Options

  1. Aa + b + c
  2. Ba +2 b
  3. Ca + c
  4. Da +2 b + c 2

Correct answer

B. a +2 b

Step-by-step solution

Let, O A =2 a +3 b - c , O B =3 a +4 b -2 c O C = a -2 b +3 c , and O D = a -6 b +6 c The vector equation of line joining the points A and B is aligned r & = O A +t( O B - O A ), t R & =(2 a +3 b - c )+t(3 a +4 b -2 c )-(2 a +3 b - c )] aligned Vector equation of the line joining the points C and D is aligned r & = O C +s( O D - O C ) & = a -2 b +3 c +s( a -6 b +6 c )-( a -2 b +3 c ) aligned Comparing coefficient of a in Eq. (ii) and (iii) we get 2+t=1 t=-1 Put in Eq. (i) aligned r & =2 a +3 b - c +(-1)[ a + b - c

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