Find the lengths of the medians of the triangle with vertices `A(0,0,6),\ B(0,4,0)a n d\ C(6,0,0)dot`

Answer

N/a

Explanation

Given that, `A-=(0,0,6),B-=(0,4,0),(C-=(6,0,0)`
Let D, E and F are the mid-points of sides BC, CA and AB respectively of `DeltaABC`.
Coordinates of `D=((0+6)/(2)(4+0)/(2),(0+0)/(2))=(3,2,0)`
Coordinates of `E=((0+6)/(2),(0+0)/(2),(6+0)/(2))=(3,0,3)`
Coordinates of `F=((0+0)/(2),(0+4)/(2),(6+0)/(2))=(0,2,3)`
Now, median `AD=sqrt((3-0)^(2)+(2-0)^(2)+(0-6)^(2))`
`=sqrt(9+4+36)=sqrt(34)`
and median `CF=sqrt((6-0)^(2)+(0-2)^(2)+(0-3)^(2))`
`=sqrt(36+4+9)=7`
`therefore` The medians of `DeltaABC` are `7, sqrt(34)` and 7 units.