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JEE Main20248 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Let a =4 i - j + k , b =11 i - j + k and c be a vector such that ( a + b ) c = c (-2 a +3 b ) . If (2 a +3 b ) c =1670 , then | c |^2 is equal to :

Options

  1. A1609
  2. B1618
  3. C1600
  4. D1627

Correct answer

B. 1618

Step-by-step solution

aligned & ( a + b ) c - c (-2 a +3 b )=0 & ( a + b ) c +(-2 a +3 b ) c =0 & ( a + b )-2 a +3 b ) c =0 & c = (4 b - a ) & = (44 i -4 j +4 k -4 i + j - k ) & = (40 i -3 j +3 k ) aligned Now aligned & (8 i -2 j +2 k +33 i -3 j +3 k ) (40 i -3 j +3 k )=1670 & (41 i -5 j +5 k ) (40 i -3 j +3 k ) =1670) & (1640+15+15) =1670 =1 & so c =40 i -3 j -3 k & | c |^2=1600+9+9=1618 aligned

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