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AP EAMCET20227 Jul 2022Evening ShiftMathematicsVector AlgebraActual

The vector x is perpendicular to the vectors a =3 i +2 j +2 k , b =18 i -22 j -5 k and make an obtuse angle with j . If | x |=14 , then x =

Options

  1. A8 i +12 j +24 k
  2. B-8 i +6 j +24 k
  3. C8 i -12 j -24 k
  4. D-8 i -12 j +24 k

Correct answer

D. -8 i -12 j +24 k

Step-by-step solution

a =3 i +2 j +2 k , b =18 i -22 j -5 k x is perpendicular to a and b . x is parallel to ( a b ) . Now, a b = | array ccc i & j & k 3 & 2 & 2 18 & -22 & -5 array | a b =34 i +51 j -102 k As x makes obtuse angle with j , coefficient of j should be negative. aligned x & =k(-2 i -3 j +6 k ), k>0 | x | & =k 4+9+36 & =7 k=14 k=2 x & =-4 i -6 j +12 k & x =-8 i -12 j +24 k aligned

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