Given, the position vector of vertex A=2i+6j+4k and centroid of ∆ABC=2i+4j+2k We know that the median AM of ∆ABC divided by centroid G, in the ratio 2: 1 .
Then, by section formula
(2,4,2)={
2x+2
2+1
,
2y+6
2+1
,
2z+4
2+1
}
On comparing, ⇒2x+2=6 ⇒x=2 ⇒2y+6=12 ⇒y=3 ⇒2z+4=6 ⇒z=1 So, the position vector of M i.e., mid point of BC is =2i+3j+k