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Question
If `vec"a"` and `vec"b"` are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.
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Solution
Given that BC = 1.5 BA
⇒ `"BC"/"BA"` = 1.5 = `3/2`
⇒ `(vec"c" - vec"b")/(vec"a" - vec"b") = 3/2`
⇒ `2vec"c" - 2vec"b" = 3vec"a" - 3vec"b"`
⇒ `2vec"c" = 3vec"a" - 3vec"b" + 2vec"b"`
⇒ `2vec"c" = 3vec"a" - vec"b"`
∴ `vec"c" = (3vec"a" - vec"b")/2`
Hence, the required vector is `vec"c" = (3vec"a" - vec"b")/2`.
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