Position vector of \(A\equiv 4\hat{i}+5\hat{j}+\hat{k};\)
Position vector of \(B\equiv -\hat{j}-\hat{k}\)
Position vector of \(C\equiv 3\hat{i}+9\hat{j}+4\hat{k};\)
Position vector of \(D\equiv -4\hat{i}+4\hat{j}+4\hat{k}\)
Hence, \(\vec{AB},\vec{AC}\) and \(\vec{AD}\) are coplanar i.e., points A, B, C, D are coplanar.
[Note: Three vectors \(\vec{a},\vec{b},\vec{c}\) are coplanar, if the scalar triple product of these three vectors is zero.]