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AP EAMCET202317 May 2023Morning ShiftMathematicsVector AlgebraActual

Let a , b and c be any three non coplanar vectors. If m , n are scalars such that a + b =m d - c and b + c =n a - d , then 3 a +2 b +2 c + d =

Options

  1. Aa - d
  2. Ba + d
  3. C0
  4. Db + c +2 d

Correct answer

A. a - d

Step-by-step solution

a + b =m d - c a + b + c =m d ...(i) & b + c =n a - d d =n a +(- b + c )...(ii) From equations (i) & (ii), we get aligned & ( a + b + c )=m(n a - b - c ) & (1-m n) a +(1+m) b +(1+m) c =0 aligned a , b and c are non-coplaner vectors 1=m n and 1+m=0 m=-1 n=-1 Putting the value of m in equation (1) a + b + c =- d a + b + c + d =0 Now, 3 a +2 b +2 c + d =( a + b + c + d )+( a + b + c )+ a =0+(- d )+ a = a - d

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