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Let a , b and c be three non-zero vectors such that no two of these are collinear. If the vector a +2 b is collinear with c and b +3 c is collinear with a ( being some non-zero scalar) then a +2 b +6 c equals

Options

  1. Aa
  2. Bb
  3. Cc
  4. D0

Correct answer

D. 0

Step-by-step solution

( a +2 b)=t₁ c and b +3 c =t₂ a (1)-2 (2) a (1+2 t₂ )+ c (-t₁-6 )=0 1+2 t₂=0 t₂=-1 / 2 & t₁=-6 . Since a and c are non-collinear. Putting the value of t₁ and t₂ in (1) and (2), we get a +2 b +6 c = 0

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