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MHT CET202020 Oct 2020Morning ShiftMathematicsVector AlgebraActual

If the position vectors of the vertices A, B, C of a tringle A B C are 4 +7 j+8 k , 2 +3 +4 k and 2 +5 +7 k respectively, then the position vector of the point where bisector of angle A meets B C is

Options

  1. A1 3 (6 +11 +15 k )
  2. B1 2 (4 +8 +11 k )
  3. C1 4 (8 +14 +19 k )
  4. D1 3 (6 +13 j +18 k )

Correct answer

D. 1 3 (6 +13 j +18 k )

Step-by-step solution

Suppose the bisector of angle A meets BC at D . Then A D divides B C in the ratio A B : A C Position vector of D = ( AC )(2 i +3 j +4 k )+( AB )(2 i +5 j +7 k ) ( AB )+( AC ) AB =-2 i -4 j -4 k and AC =-2 i -2 j - k | AB |= AB =6 and | AC |= AC = 4+4+1 =3 Position vector of D= 6(2 i +3 j +4 k )+3(2 i +5 j +7 k ) 6+3 = 18 i +33 j +45 k 9 = 1 3 (6 i +11 j +15 k )

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