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Show that the points A(2,1,-1),B(0,-1,0)...

Show that the points A(2,1,-1),B(0,-1,0),C(4,0,4) and (2,0,1) are coplanar.

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To show that the points A(2,1,-1), B(0,-1,0), C(4,0,4), and D(2,0,1) are coplanar, we can use the concept of the scalar triple product. The points are coplanar if the scalar triple product of the vectors formed by these points is zero. ### Step-by-Step Solution: 1. **Determine the Position Vectors**: - Let \( \vec{A} = 2\hat{i} + 1\hat{j} - 1\hat{k} \) - Let \( \vec{B} = 0\hat{i} - 1\hat{j} + 0\hat{k} \) - Let \( \vec{C} = 4\hat{i} + 0\hat{j} + 4\hat{k} \) ...
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