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MHT CET2008MathematicsVector Algebra

The line joining the points 6 a -4 b +4 c ,-4 c and the line joining the points - a -2 b -3 c , a +2 b -5 c intersect at

Options

  1. A-4 a
  2. B4 a - b - c
  3. C4 c
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

The equations of the lines joining 6 a -4 b +4 c ,-4 c and - a -2 b -3 c , a +2 b -5 c are respectively r =6 a -4 b +4 c +m(-6 a +4 b -8 c ) ...(i) and r =- a -2 b -3 c +n(2 a +4 b -2 c ) ...(ii) For the point of intersection, the Eqs. (i) and (ii) should give the same value of r . Hence equating the coefficients of vectors a , b and c in the two expressions for r , we get array l 6 m+2 n=7 2 m-2 n=1 array and 8 m-2 n=7 On solving Eqs. (iii) and (iv), we get m=1, n= 1 2 . These values of m and n , also satisfy the

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