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

Options

A. 3:2 internally
B. 3:2 externally
C. 2:3 internally
D. 2:3 externally

Answer

A

Explanation

Given , ` 2veca +3 vecb-5 vec(c)=0`
`implies ( 2 veca+3 vecb)/(5)=vecc`
`implies(2 veca+3 vecb)/(2+3)=vec(c)`
`implies (veca+(3)/(2)vecb)/(1+(3)/(2))=vec(c)`..........(i)
Let `vec(c)` divide `vec(AB)` in the ratio ` lambda:1`
Then ` vecc=(vec a + lambda vecb)/(1+ lambda )` ............(ii)
On comparig Eqs. (i) and (ii) ,we get ` lambda=(3)/(2)`
`:.` Required ratio is ` 3:2 ` internally .