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Question
The position vector of the point which divides the join of points with position vectors `vec"a" + vec"b"` and 2`vec"a" - vec"b"` in the ratio 1:2 is ______.
Options
`(3vec"a" + 2vec"b")/3`
`vec"a"`
`(5vec"a" - vec"b")/3`
`(4vec"a" + vec"b")/3`
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Solution
The position vector of the point which divides the join of points with position vectors `vec"a" + vec"b"` and 2`vec"a" - vec"b"` in the ratio 1:2 is `(4vec"a" + vec"b")/3`.
Explanation:
Applying section formula the position vector of the required point is
`(2(vec"a" + vec"b") + 1(2vec"a" - vec"b"))/(2 + 1) = (4vec"a" + vec"b")/3`
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