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JEE Main202524 Jan 2025Morning ShiftMathematicsVector AlgebraActual

Let a = i +2 j +3 k , b =3 i + j - k and c be three vectors such that c is coplanar with a and b . If the vector C is perpendicular to b and a c =5 , then | c | is equal to

Options

  1. A11 6
  2. B1 3 2
  3. C16
  4. D18

Correct answer

A. 11 6

Step-by-step solution

aligned & c = ( b ( a b )) & = (( b b ) a -( a b ) b ) & = (11 a -2 ~b )= (11 i +22 j +33 k -6 i -2 j +2 k ) & = (5 i +20 j +35 k ) & =5 (5 i +4 j +7 k ) & = Given c a =5 & =5 (1+8+21)=5 = = 1 30 & c = 1 6 ( i +4 j +7 k ) & c = 1+16+49 6 = 11 6 aligned

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