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JEE Main20244 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Let a = i + j + k , b =2 i +4 j -5 k and c =x i +2 j +3 k , x R . If d is the unit vector in the direction of b + c such that a d =1 , then ( a b ) c is equal to

Options

  1. A11
  2. B3
  3. C9
  4. D6

Correct answer

A. 11

Step-by-step solution

aligned & d = ( b + c ) & a d = ( b a + c a ) & 1= (1+ x +5) aligned 1= (x+6) ...(1) aligned & | d |=1 & | ( b + c )|=1 & | (( x +2) i +6 j -2 k )|=1 & ^2 (( x +2)^2+6^2+2^2 )=1 & x ^2+4 x +4+36+4=( x +6)^2 & x ^2+4 x +44= x ^2+12 x +36 & 8 x =8, x =1 & | array ccc 1 & 1 & 1 2 & 4 & -5 x & 2 & 3 array |=( a b ) c & | array ccc 0 & 0 & 1 -2 & 9 & -4 x -2 & -1 & 3 array |=2-9( x -2) & =20-9 x & at x =1 & 20-9=11 aligned

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