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Paragraph: The position vectors of two points A and B are i - j and j + k respectively. Question: Consider the following points: 1. (-1,-3,1) 2. (-1,3,2) 3. (-2,5,3) Which of the above points lie on the line joining A and B ?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

B. 2 and 3 only

Step-by-step solution

A( i - j ) and B( j + k ) Equation of A B =( j + k )-( i - j )=- i +2 j + k Direction ratio of line parallel to A B=(-1,2,1) . Equation of line passing through A and pass through A B , x-1 -1 = y+1 2 = z-0 1 Clearly (-1,3,2) and (-2,5,3) is satisfying i.e. only 2 and 3.

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