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AP EAMCET202421 May 2024Morning ShiftMathematicsVector AlgebraActual

c is a vector along the bisector of the internal angle between the vectors a =4 i +7 j -4 k and b =12 i -3 j +4 k . If the magnitude of c is 3 13 then c =

Options

  1. A5 i -8 j +2 2 k
  2. B10 i +4 j - k
  3. Ci -10 j +4 k
  4. D2 2 i +5 j -8 k

Correct answer

B. 10 i +4 j - k

Step-by-step solution

aligned & (b) a =4 i +7 j -4 k , b =12 i -3 j +4 k & U _ a = 4 i +7 j -4 k 9 , U _ b = 12 i -3 j +4 k 13 aligned unit vector along bisector of vector a and b is aligned & U _ c =k ( U _ a + U _ b ) & U _ c =k ( 160 i +64 j -16 k 117 ) or k ( -56 i +64 j -88 k 117 ) & U _ c = 16 k 117 (10 i +4 j - k ) or 8 k 117 (-7 i +8 j -11 k ) aligned Since magnitude of c =3 13 c =10 i +4 j - k

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