Word Count : 410

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To find the vector equation of the plane determined by three points \((1, 0, -1)\), \((0, 1, 1)\), and \((-1, 1, 0)\), we can follow these steps: 1. Find two vectors that lie on the plane. We can use the given points to create two vectors in the plane by subtracting the coordinates of one point from another. \[ \mathbf{v_1} = (0, 1, 1) - (1, 0, -1) = (-1, 1, 2) \] \[ \mathbf{v_2} = (-1, 1, 0) - (1, 0, -1) = (-2, 1, 1) \] 2. Find the normal vector to the plane. The normal vector \(\mathbf{n}\) to the ______ _______ _______ ___ ___ ______ ________ ______ ________ ________ _____ ____.
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