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Manipal MET2018MathematicsThree Dimensional Geometry

If a , b , c are the position vectors of A, B, C respectively such that 3 a +4 b -7 c = 0 , then C divides A B in the ratio

Options

  1. A4:3
  2. B4;7
  3. C3:7
  4. D3:4

Correct answer

A. 4:3

Step-by-step solution

Let C divides A B in the ratio m: 1 . Then c = m b + a m+1 array lr & m c + c =m b + a & a +m b -m c - c = 0 & a +m b +(-m-1) c = 0 ...(i) array Given, array ll Given, & 3 a+4 b-7 c=0 & a+ 4 3 b- 7 3 c=0...(ii) array On comparing Eqs. (i) and (ii), we get m= 4 3 Required ratio is 4: 3

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