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 ______.

पर्याय

• `4vec"a" - 2vec"b" + 2vec"c"`

• `4vec"a" + 2vec"b" + 2vec"c"`

• `-4vec"a" + 2vec"b" + 2vec"c"`

• `4vec"a" - 2vec"b" - 2vec"c"`

Answer 1

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"`