Question

If `vec(AB)=hatj+hatk` and `vec(AC)=3hati-hatj+4hatk` represent the two vectors along the sides AB and AC of ΔABC, prove that the median `vec(AD)=(vec(AB)+vec(AC))/2`, where D is midpoint of BC. Hence, find the length of median AD.

Answer 1

`veca=0`

`vecb= vec(AB)`

`vecc=vec(AC)`

`vecd=(vecb+vecc)/2`

= `(hatj+hatk+3hati-hatj+4hatk)/2`

= `(3hati)/2+(5hatk)/2`

`vecAD=vecd-veca`

`3/2hati+5/2hatk`

`|vecAD|=sqrt((3/2)^2+(5/2)^2)`

= `sqrt(9/4+25/4)`

= `sqrt(34/4)`

= `sqrt34/2`