Question: if abcd is a parallelogram find the coordinates of d?
Answer: If you have a parallelogram ABCD, then you know the vectors →AB and →DC need to be equal as they are parallel and have the same length. Since we know that →AB=(−2,3,−6) you can easily calculate D since you (now) know C and →CD(=−→AB). We get for →0D=→0C+→CD=(−1,1,2)+(2,−3,6)=(1,−2,8) and hence D(1,−2,8).