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AP EAMCET201920 Apr 2019Morning ShiftMathematicsStraight LinesActual

If (4 i +7 j +8 k , 2 i +3 j +4 k , 2 i +5 j +7 k ) are respectively the position vectors of the vertices (A, B, C ) of ( A B C ), then the position vector of the point where the bisector of angle (A ) meet ( B C ) is

Options

  1. A(2 i + 13 3 j +2 k )
  2. B(2 i - 13 3 j +6 k )
  3. C(2 i +13 j +6 k )
  4. D(2 i + 13 3 j +6 k )

Correct answer

D. (2 i + 13 3 j +6 k )

Step-by-step solution

As we know bisector of angle (A ) divides the (B C ) in ratio (c: b ). where (c ) is length of side (A B= 4+16+16 =6 ) and (b ) is length of side (A C= 4+4+1 =3 ) ( ) Position vector of the point where the bisector of angle (A ) meet ( B C ) is ( aligned & 6(2 i +5 j +7 k )+3(2 i +3 j +4 k ) 6+3 & = 18 i +39 j +54 k 9 =2 i + 13 3 j +6 k aligned ) Hence, option (4) is correct.

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