Three consective vertices of a parallelogram ABCD are A ( 6, -2 ,4) , B ( 2, 4,-8) and C (-2,2,4) . Find the condinates of the following

Explanation

let the coordinates of the fourth vertices D ( x,y,z).
Mid- points of diagonal AC.
`x=(x_(1)+x_(2))/2,y=(y_(1)+y_(2))/2,z=(z_(1)+z_(2))/2`
and `x= (6-2)/2=2,y=(-2+2)/2=0, x=(4+4)/2=4`
since , the mid point of AC are ( 2,0,4)
now, mid piont of BD . `2= (x+2)/3 Rightarrowx=2`
`0=(y+4)/2Rightarrow y=-4`
` 4=(z-8)/2Rightarrow z=16)`
So, the coordinates of fourth vertex D is ( 2,-4,16).