Let `G` be the centroid of `\ A B Cdot` If ` vec A B= vec a ,\ vec A C= vec b ,` then the bisector ` vec A G ,` in terms of ` vec a\ a n d\ vec b` is `2/3( vec a+ vec b)` b. `1/6( vec a+ vec b)` c. `1/3( vec a+ vec b)` d. `1/2( vec a+ vec b)1`

Explanation

Let A as origin.
After that position vectors of `A, B, C` we have ` 0 , a` and `b` respectively.


centroid `G` has position vector



`frac{0+a+b}{3}=frac{a+b}{3} `

`
therefore A G=frac{a+b}{3}`