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, 2a + 3b - 5c = 0
`implies (2a+3b)/(5)=c`
`implies (2a+3b)/(2+3)=c`
`implies (a+(3)/(2)b)/(1+(3)/(2))=c" ...(i)"`
Let c divides AB in the ratio `lambda : 1`.
Then, `c=(a+lambdab)/(1+lambda)" ... (ii)"`
On comparing Eqs. (i) and (ii), we get `lambda = (3)/(2)`
So, required ratio is 3 : 2 internally.