Q.7 If a, b, c are the position vectors of points A, B, C respectively and 10a = 7b + 3c then find the ratio in which the point C divides the line segment AB .

Answer: C divides AB externally in the ratio 7 : 10. From 10a = 7b + 3c : 3c = 10a - 7b , so c = 7b - 10a/7 - 10 . This is the section formula for external division, c = mb - na/m - n , with m = 7,\ n = 10 . Hence C divides AB externally in the ratio 7 : 10 .

If \(\bar{a}, \bar{b}, \bar{c}\) are the position vectors of points \(A, B, C\) respectively and \(10\bar{a} = 7\bar{b} + 3\bar{c}\) then find the ratio in which the point \(C\) divides the line segment \(AB\).

Q.7 If \(\bar{a}, \bar{b}, \bar{c}\) are the position vectors of points \(A, B, C\) respectively and \(10\bar{a} = 7\bar{b} + 3\bar{c}\) then find the ratio in which the point \(C\) divides the line segment \(AB\).

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Answer: C divides AB externally in the ratio 7 : 10.

From \(10\bar{a} = 7\bar{b} + 3\bar{c}\): \(3\bar{c} = 10\bar{a} - 7\bar{b}\), so

\(\bar{c} = \frac{7\bar{b} - 10\bar{a}}{7 - 10}\).

This is the section formula for external division, \(\bar{c} = \frac{m\bar{b} - n\bar{a}}{m - n}\), with \(m = 7,\ n = 10\). Hence C divides AB externally in the ratio \(7 : 10\).

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If \(\bar{a}, \bar{b}, \bar{c}\) are the position vectors of points \(A, B, C\) respectively and \(10\bar{a} = 7\bar{b} + 3\bar{c}\) then find the ratio in which the point \(C\) divides the line segment \(AB\).

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