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AP EAMCET20225 Jul 2022Evening ShiftMathematicsVector AlgebraActual

Let O A =-4 i +3 k , O B =14 i +2 j -5 k O D bisects A O B and | O D |= 6 , then O D =

Options

  1. A( i + j +2 k )
  2. B( i +2 j + k )
  3. C(2 i + j + k )
  4. D1 2 (2 i + j + 7 k )

Correct answer

A. ( i + j +2 k )

Step-by-step solution

Considering O A and O B as adjacent sides of a parallogram. O D will be along diagonal. Equation of diagonal aligned & = ( a | a | + b | b | ) & = ( -4 i +3 k 4^2+3^2 + 14 i +2 j -5 k 14^2+2^2+5^2 ) & = ( -4 i +3 k 5 + 14 i +2 j -5 k 15 ) aligned aligned & = 15 (2 i +2 j +4 k ) & = 2 15 ( i + j +2 k ) aligned | O D |= 6 2 15 1^2+1^2+2^2 = 6 2 15 =1 Equation of O D is ( i + j +2 k )

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