ok the ques is -

The points A,B,C in R^3 are position vectors

a=(1,1,2)b=(2,-1,4)c=(2,1,5)

a) write down the vectors AB and AC

b) Hence or otherwise find the position vector of the point D such that ABCD is a parallelogram.

solution -

i solved for

a) AB=(1,-2,2) and AC=(1,0,3)

b) ok the answer differs from my answer but this is what i said -

using the definition of vector addition,

a+b=c

AB=-DC=-(1,-2,2)

AC=(1,0,3)

DC + AD = AC

-(1,-2,3) + (x,y,z) =(1,0,3)

therefore,

(x,y,z) = (2,-2,5)

am i incorrect for ques (b)??

the answer was different!