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Let L₁: x-6 3 = y-7 -1 = z-4 1 and L₂: x -3 = y+9 2 = z-2 4 . If L₁ & L₂ are skew lines such that P & Q are two points nearest to each other lying on lines L₁ & L₂ respectively. If image of P with respect to plane 3 x+3 y-z=11 is R(a, b, c) , then (a+b+c) equals

Correct answer

4

Step-by-step solution

direction ratio of gathered PQ (-3 r ₂-3 r ₁-6,2 r ₂+ r ₁-16,4 r ₂- r ₁-2 ) Now, -3 (-3 r ₂-3 r ₁-6 )+2 (2 r ₂, r ₁-16 ) +4 (4 r ₂- r ₁-2 )=0 gathered aligned & 7 r₁+29 r₂=22 & 3 (-3 r₂-3 r₁-6 )- (2 r₂+r₁-16 )+ (4 r₂-r₁-2 )=0 & 7 r₁+29 r₂=22 aligned ...(1) gathered 3 (-3 r₂-3 r₁-6 )- (2 r₂+r₁-16 )+ (4 r₂-r₁-2 )=0 11 r₁+7 r₂=-4 gathered ...(2) On solving (1) & (2) aligned & r₁=-1, r₂=1 & so P(3,8,3) aligned Image of P (3,8,3) w.r.t Plane 3 x+3 y-z=11 aligned & R (-3,2,5) & a + b + c =4 aligned

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