The position vector of the point which divides the join of points 2vec"a" - 3vec"b" and vec"a" + vec"b" in the ratio 3:1 is ______.

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The position vector of the point which divides the join of points 2vec"a" - 3vec"b" and vec"a" + vec"b" in the ratio 3:1 is (5vec"a")/4. Explanation: The given vectors are 2vec"a" - 3vec"b" and vec"a" + vec"b" in the ratio 3:1. $\therefore$ The position vector of the required point c which divides the join of the given vectors vec"a" and vec"b" is `vec"c" = ("m"_1x_2 + "m"_2x_1)/("m"_1 + "m"_2) = (1 * (2vec"a" - 3vec"b") + 3(vec"a" + vec"b))/(3 + 1) = (2vec"a" - 3vec"b" + 3vec"a" + 3vec"b")/4 = (5vec"a")/4 = $\frac{5}{4}$ vec"a"`

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