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The position vector of a point which divides the segment joining 2a-3b and 3a-2b in the ratio 2:3 internally is
  • a)
    (12/5)a+(13/5)b
  • b)
    [(12a-13b)/5]
  • c)
    [(-12a+13b)/5]
  • d)
    none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The position vector of a point which divides the segment joining 2a-3b...
Solution:

Let P be the point which divides the segment joining 2a-3b and 3a-2b in the ratio of 2:3.

Let the position vector of P be r.

Then, r = (2/5)(3a-2b) + (3/5)(2a-3b)

r = (6/5)a - (4/5)b + (6/5)a - (9/5)b

r = (12/5)a - (13/5)b

Therefore, the correct answer is option 'B'.
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The position vector of a point which divides the segment joining 2a-3b and 3a-2b in the ratio 2:3 internally isa)(12/5)a+(13/5)bb)[(12a-13b)/5]c)[(-12a+13b)/5]d)none of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
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