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L and M are two points with positive vec...

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

A

`3vecb`

B

`4vecb`

C

`5vecb`

D

`3veca+4vecb`

Text Solution

Verified by Experts

The correct Answer is:
C
Given,
`L=2veca-vecb`
and `M=veca+2vecb`
Since, N divides LM in the ratio 2:1 externaly.
`therefore` Position vector of N
`=(2(veca+2vecb)-1(2veca-vecb))/(2-1)`
`=(2veca+4vecb-2veca+vecb)/91)=5vecb`
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