The vector equation of the plane through the point and passing through the line of…

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The vector equation of the plane through the point (2,1,−1)(2, 1, -1) and passing through the line of intersection of the plane r⋅(i^+3j^−k^)=0\mathbf{r} \cdot (\hat{i} + 3\hat{j} - \hat{k}) = 0 and r⋅(j^+2k^)=0\mathbf{r} \cdot (\hat{j} + 2\hat{k}) = 0 , is (1) r⋅(i^+9j^+11k^)=0\mathbf{r} \cdot (\hat{i} + 9\hat{j} + 11\hat{k}) = 0 (2) r⋅(i^+9j^+11k^)=6\mathbf{r} \cdot (\hat{i} + 9\hat{j} + 11\hat{k}) = 6 (3) r⋅(i^−3j^−13k^)=0\mathbf{r} \cdot (\hat{i} - 3\hat{j} - 13\hat{k}) = 0 (4) None of these

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