Q.7 If a, b, c are the 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 segment BA .

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

Q.7 If \(\bar{a}, \bar{b}, \bar{c}\) are the position vectors of the points \(A, B, C\) respectively and \(5\bar{a} - 3\bar{b} - 2\bar{c} = \bar{0}\), then find the ratio in which the point \(C\) divides the line segment \(BA\).

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

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Answer: \(C\) divides \(BA\) externally in the ratio \(5 : 3\).

\(5\bar{a} - 3\bar{b} = 2\bar{c}\), so \(\bar{c} = \frac{5\bar{a} - 3\bar{b}}{2} = \frac{5\bar{a} - 3\bar{b}}{5 - 3}\).

By the section formula for external division, the point dividing \(BA\) externally in the ratio \(m : n\) has position vector \(\frac{m\bar{a} - n\bar{b}}{m - n}\). Comparing, \(m = 5\), \(n = 3\).

Hence \(C\) divides the segment \(BA\) externally in the ratio \(5 : 3\).

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

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