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AP EAMCET202318 May 2023Evening ShiftMathematicsVector AlgebraActual

Let a , b , c be co-initial vectors and a =2 i - j +5 k and b =3 i +7 j - k . Let ( a , b )= be an acute angle and c be the vector along the bisector of the angle . If , x , y R , then c =

Options

  1. A(5 i +6 j +4 k )
  2. B(- i -8 j +6 k )
  3. C(2 x+3 y) i +(7 y-x) j +(5 x-y) k
  4. D(2 x+3 y) i +(x+7 y) j +(5 x+y) k

Correct answer

C. (2 x+3 y) i +(7 y-x) j +(5 x-y) k

Step-by-step solution

a =2 i - j +5 k , b =3 i +7 j - k Now, the angle bisector of vector a & b are aligned & c =| a | b + a | b | & = 30 (3 i +7 j - k )+(2 i - j +5 k ) 59 aligned + Let 30 = y & 59 = x then aligned & c =(3 y i +7 y j -y k )+(2 x i -x j +5 x k ) & c =(3 y+2 x) i (7 y-x) j +(5 x-y) k aligned

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