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If 2veca+ 3vecb-5 vecc=vec0, then rati...

If ` 2veca+ 3vecb-5 vecc=vec0`, then ratio in which ` vecc` divides ` vec(AB)` is

A

`3 : 2` internally

B

`3 : 2` externally

C

`2 : 3` internally

D

`2 : 3` externally

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `2a+3b-5c=-0`
`rArr" "(2a+3b)/5=c`
`rArr" "(2a+3b)/(2+3)=c`
`rArr" "(a+3/2b)/(1+3/2)=c" ...(1)"`
Let c divides AB in the ratio `lamda:1`
`"Then, "c=(a+lamdab)/(1+lamda)" …(ii)"`
On comparing (i) and (ii), we get `lamda=3/2`
`:." "` Required ratio is 3 : 2 internally.
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