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JEE Main20245 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Let a =2 i +5 j - k , b =2 i -2 j +2 k and c be three vectors such that ( c + i ) ( a + b + i )= a ( c + i ) . If a c =-29 , then c (-2 i + j + k ) is equal to:

Options

  1. A15
  2. B12
  3. C10
  4. D5

Correct answer

D. 5

Step-by-step solution

Let's assume aligned v & = a + b + i & =5 i +3 j + k aligned and c + i = p So, aligned & p v = a p & p v + p a = 0 & p ( v + a )= 0 & p = ( v + a ) & c + i = (7 i +8 j ) & a c + a i = a (7 i +8 j ) & -29+2= (14+40) & =- 1 2 aligned gathered c (-2 i + j + k )+ i (-2 i + j + k )= (7 i +8 j ) (-2 i + j + k ) =- 1 2 (-14+8)+2=5 gathered

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