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MHT CET202411 May 2024Evening ShiftMathematicsVector AlgebraActual

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 , then a +2 ~b +6 c equals

Options

  1. Ac ( being some non-zero scalar)
  2. Bb ( being some non-zero scalar)
  3. Ca ( being some non-zero scalar)
  4. D0 ( being some non-zero scalar)

Correct answer

D. 0 ( being some non-zero scalar)

Step-by-step solution

a +2 ~b is collinear with c a +2 b =n c ...(i) Similarly b +3 c = m a ...(ii) m and n are non-zero scalars. (i) a +2 ~b +6 c =( n +6) c (ii) a +2 b +6 c =(2 m+1) a n +6=0 and 2 ~m +1=0 n =-6 and m = -1 2 (i) a +2 b +6 c =0

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