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Problem Equation of the plane that contains the lines r = ( i ^ + j ^ ) + λ ( i ^ + 2 j ^ − k ^ ) \mathbf{r} = (\hat{i} + \hat{j}) + \lambda(\hat{i} + 2\hat{j} - \hat{k}) r = ( i ^ + j ^ ) + λ ( i ^ + 2 j ^ − k ^ ) r = ( i ^ + j ^ ) + μ ( − i ^ + j ^ − 2 k ^ ) \mathbf{r} = (\hat{i} + \hat{j}) + \mu(-\hat{i} + \hat{j} - 2\hat{k}) r = ( i ^ + j ^ ) + μ ( − i ^ + j ^ − 2 k ^ ) r ⋅ ( 2 i ^ + j ^ − 3 k ^ ) = − 4 \mathbf{r} \cdot (2\hat{i} + \hat{j} - 3\hat{k}) = -4 r ⋅ ( 2 i ^ + j ^ − 3 k ^ ) = − 4 r × ( − i ^ + j ^ + k ^ ) = 0 \mathbf{r} \times (-\hat{i} + \hat{j} + \hat{k}) = 0 r × ( − i ^ + j ^ + k ^ ) = 0 r ⋅ ( − i ^ + j ^ + k ^ ) = 0 \mathbf{r} \cdot (-\hat{i} + \hat{j} + \hat{k}) = 0 r ⋅ ( − i ^ + j ^ + k ^ ) = 0 Browse the problem library