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Problem Equation of the plane through three points A , B A, B A , B C C C − 6 i + 3 j + 2 k -6\mathbf{i} + 3\mathbf{j} + 2\mathbf{k} − 6 i + 3 j + 2 k 3 i − 2 j + 4 k 3\mathbf{i} - 2\mathbf{j} + 4\mathbf{k} 3 i − 2 j + 4 k 5 i + 7 j + 3 k 5\mathbf{i} + 7\mathbf{j} + 3\mathbf{k} 5 i + 7 j + 3 k r ⋅ ( i − j + 7 k ) + 23 = 0 \mathbf{r} \cdot (\mathbf{i} - \mathbf{j} + 7\mathbf{k}) + 23 = 0 r ⋅ ( i − j + 7 k ) + 23 = 0 r ⋅ ( i + j + 7 k ) = 23 \mathbf{r} \cdot (\mathbf{i} + \mathbf{j} + 7\mathbf{k}) = 23 r ⋅ ( i + j + 7 k ) = 23 r ⋅ ( i + j − 7 k ) + 23 = 0 \mathbf{r} \cdot (\mathbf{i} + \mathbf{j} - 7\mathbf{k}) + 23 = 0 r ⋅ ( i + j − 7 k ) + 23 = 0 r ⋅ ( i − j − 7 k ) = 23 \mathbf{r} \cdot (\mathbf{i} - \mathbf{j} - 7\mathbf{k}) = 23 r ⋅ ( i − j − 7 k ) = 23 Browse the problem library