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Show that four points A, B, C and D whose position vectors are \(4\hat{i}+5\hat{j}+\hat{k}\) \(-\hat{j}-\hat{k},\) \(3\hat{i}+9\hat{j}+4\hat{k}\) and \(4(-\hat{i}+\hat{j}+\hat{k})\) respectively are coplanar.

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Position vector of \(A = 4\hat{i}+5\hat{j}+\hat{k}\) and Position vector of \(B = -\hat{j}-\hat{k}\)

Position vector of \(C = 3\hat{i}+9\hat{j}+4\hat{k}\) and Position vector of \(D=4(-\hat{i}+\hat{j}+\hat{k})\)

\(\Rightarrow \vec{AB},\vec{AC}\) and \(\vec{AD}\) are coplanar.

\(\Rightarrow A, B, C, D\) are coplanar.

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