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AP EAMCET202125 Aug 2021Evening ShiftMathematicsVector AlgebraActual

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

Options

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

Correct answer

D. 0

Step-by-step solution

Given a, b and c are non zero vectors such that no two of these are collinear. a + 2b is collinear with c and b + 3c is collinear with a. To Find a + 2b + 6c Since, a + 2b is collinear with c. a +2 b =m c ...(i) where m is non zero scalar. and b + 3c = na … (ii) Multiply by 2 in Eq. (ii) and subtracting from Eq. (i), a + 2b − 2b − 6c = mc − 2na a − 6c = mc − 2na On comparing both sides m=-6 and n= -1 2 From Eq. (i), we get a + 2b = mc a + 2b = − 6c a+2 b+6 c=0

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