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AP EAMCET2007MathematicsThree Dimensional Geometry

The ratio in which i +2 j +3 k divides the join of -2 i +3 j +5 k and 7 i - k is

Options

  1. A2: 1
  2. B2: 3
  3. C3: 4
  4. D1: 4

Correct answer

A. 2: 1

Step-by-step solution

Let the line joining the points with position vectors -2 i +3 j +5 k and 7 i - k be divide in the ratio : 1 by i +2 j +3 k . aligned & (7 i - k )+(-2 i +3 j +5 k ) +1 = i +2 j +3 k & (7 -2) i +3 j +(5- ) k =( +1) i & +2( +1) j +3( +1) k & aligned On equating the coefficient of i , we get aligned & aligned & 7 -2= +1 & =2 & Hence, ratio : 1=2: 1 . aligned aligned

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