Four points A(1,0,1), B(2,1,0), C(0,2,1), D(k,1,2) are coplanar. Find k.

Question

G1 Physics · Accepted Answer

AB=(1,1,−1), AC=(−1,2,0), AD=(k−1,1,1). Coplanarity requires AB·(AC×AD)=0. This gives 3k−3=0, hence k=1.