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Question
The position vectors of points A, B, C are respectively `vec"a", vec"b", vec"c"`. If L divides AB in 3:4 and M divides BC in 2:1 both externally, then `vec("LM")` is ______.
Options
`4vec"a" - 2vec"b" + 2vec"c"`
`4vec"a" + 2vec"b" + 2vec"c"`
`-4vec"a" + 2vec"b" + 2vec"c"`
`4vec"a" - 2vec"b" - 2vec"c"`
MCQ
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Solution
The position vectors of points A, B, C are respectively `vec"a", vec"b", vec"c"`. If L divides AB in 3:4 and M divides BC in 2:1 both externally, then `vec("LM")` is `underlinebb(-4vec"a" + 2vec"b" + 2vec"c")`.
Explanation:
`vec"L" = (4vec"a" - 3vec"b")/1, vec"M" = (2vec"c" - vec"b")/1`
then `vec("LM")` = P.V of `vec"M"` – P.V of C
`vec("LM") = (2vec"c" - vec"b") - (4vec"a" - 3vec"b")`
`vec("LM") = -4vec"a" + 2vec"b" + 2vec"c"`
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Vector and Cartesian Equations of a Line - Position Vector of a Point in a Space
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