Question

L and M are two points with position vectors `2veca - vecb` and `veca + 2vecb` respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 externally is ______ 

पर्याय

• `3vecb`

• `4vecb`

• `5vecb`

• `3veca + 4vecb`

Answer 1

L and M are two points with position vectors `2veca - vecb` and `veca + 2vecb` respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 externally is `underlinebb(5vecb)`.

Explanation:

Let N`(vecn)` divide line segment LM externally in the ratio 2 : 1.

∴ `vecn = (2(veca + 2vecb) - (2veca - vecb))/(2 - 1)`

= `(2veca + 4vecb - 2veca + vecb)/1`

= `5vecb`