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JEE Main202529 Jan 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let ( a = i +2 j + k ) and ( b =2 i +7 j +3 k . ) Let ( L ₁: r =(- i +2 j + k )+ a , R ) and ( L ₂: r =( j + k )+ b , R ) be two lines. If the line ( L ₃ ) passes through the point of intersection of ( L ₁ ) and (L₂ ), and is parallel to ( a + b ), then (L₃ ) passes through the point :

Options

  1. A((5,17,4) )
  2. B((2,8,5) )
  3. C((8,26,12) )
  4. D((-1,-1,1) )

Correct answer

C. ((8,26,12) )

Step-by-step solution

aligned & L₁: r =(- i +2 j + k )+ ( i +2 j + k ) & r =( -1) i +2( +1) j +( +1) k & L ₂: r =( j + k )+ (2 i +7 j +3 k ) & r =2 i +(1+7 ) j +(1+3 ) k aligned For point of intersection equating respective components aligned & -1=2 & 2( +1)=1+7 & +1=1+3 aligned We get aligned & =3 and =1 & a + b =3 i +9 j +4 k aligned L ₃: r =2 i +8 j +4 k + (3 i +9 j +4 k ) For =2, r =8 i +26 j +12 k

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