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AP EAMCET201920 Apr 2019Morning ShiftMathematicsVector AlgebraActual

If the position vectors of the vertices of a ( A B C ) are ( O A =3 i + j +2 k , O B = i +2 j +3 k ) and ( O C =2 i +3 j + k ), then the length of the altitude of ( A B C ) drawn from (A ) is

Options

  1. A( 3 2 )
  2. B( 3 2 )
  3. C( 3 2 )
  4. D( 3 2 )

Correct answer

B. ( 3 2 )

Step-by-step solution

Since, length of altitude of ( A B C ) drawn from (A ) is ( aligned & h= ( Area of A B C) 1 2 | B C | = 1 2 | A B A C | 1 2 | B C | & A B =-2 i + j + k & A C =- i +2 j - k & and B C = i + j -2 k aligned ) ( aligned & So, A B A C = | array ccc i & j & k -2 & 1 & 1 -1 & 2 & -1 array | & = i (- l -2- j (2+1)+ k (-4+1)=-3 i -3 j -3 k & | A B A C |=3 3 and | B C |= 6 & h= 3 3 2 3 = 3 2 aligned ) Hence, option (2) is correct.

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