Maharashtra State BoardHSC Arts 12th Board Exam
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If a, b, c are the position vectors of the points A, B, C respectively and 2a+3b−5c=0, then find the ratio in which the point C divides line segment AB. - Mathematics and Statistics

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If `bara, barb, bar c` are the position vectors of the points A, B, C respectively and ` 2bara + 3barb - 5barc = 0` , then find the ratio in which the point C divides line segment  AB.

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Solution

`2bara + 3barb - 5barc = 0`

`5 barc=3barb+2bara`

`barc=(3barb+2bara)/5`

`barc=(3barb+2bara)/(3+2)`

∴C divides seg AB internally in the ratio 3 : 2

Concept: Basic Concepts of Vector Algebra
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