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

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Sum

If `bar("a"), bar("b")` and `bar("c")` are position vectors of the points A, B, C respectively and `5bar("a") - 3bar("b") - 2bar("c") = bar(0)`, then find the ratio in which the point C divides the line segement BA

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Solution

`5bar("a") - 3bar("b") - 2bar("c")` = 0

∴ `2bar("c") = 5bar("a") - 3bar("b")`

∴ `bar("c") = (5bar("a") - 3bar("b"))/2`

∴ `bar("c") = (5bar("a") - 3bar("b"))/(5 - 3)`

∴ The point C divides the line segment BA externally in ratio 5:3.

Concept: Section Formula
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