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MHT CET202520 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

If a = i + j , ~b =2 i - k then the point of intersection of the lines r a = b a and r b = a b is

Options

  1. A(3,-1,1)
  2. B(3,1,-1)
  3. C(-3,1,1)
  4. D(1,1,1)

Correct answer

B. (3,1,-1)

Step-by-step solution

Finding the intersection point requires expressing both lines in standard vector form. The first equation r a = b a simplifies to ( r - b ) a = 0 , indicating r - b is parallel to a . This yields the parametric form r = b + a . The second equation r b = a b similarly gives ( r - a ) b = 0 , producing r = a + b . Equating both expressions for r gives b + a = a + b , which rearranges to ( - 1) a = ( - 1) b . With a = i + j and b = 2 i - k , substitution yields: ( - 1) i + ( - 1) j = 2( - 1) i - ( - 1) k Comparing coe

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