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MHT CET202416 May 2024Evening ShiftMathematicsVector AlgebraActual

If a = i -2 j +3 k and b =2 i +3 j - k are two vectors, then the angle between the vectors 3 a +5 b and 5 a +3 b is

Options

  1. A⁻¹ ( 10 19 )
  2. B⁻¹ ( 11 19 )
  3. C⁻¹ ( 13 19 )
  4. D⁻¹ ( 14 19 )

Correct answer

C. ⁻¹ ( 13 19 )

Step-by-step solution

aligned 3 a +5 ~b & =3( i -2 j +3 k )+5(2 i +3 j - k ) & =13 i +9 j +4 k aligned aligned 5 a +3 ~b & =5( i -2 j +3 k )+3(2 i +3 j - k ) & =11 i - j +12 k aligned aligned & = (13 i +9 j +4 k ) (11 i - j +12 k ) 169+81+16 121+1+144 & = 13(11)+9(-1)+1(12) 266 266 aligned aligned & = 143-9+48 266 & = 182 266 & = 13 19 & = ⁻¹ ( 13 19 ) aligned

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