The vector equation of the plane through the point and perpendicular to the line of…

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

Problem

The vector equation of the plane through the point

\hat{i} + 2\hat{j} - \hat{k}

and perpendicular to the line of intersection of the plane

\mathbf{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1

and

\mathbf{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2

, is (1)

\mathbf{r} \cdot (2\hat{i} + 7\hat{j} - 13\hat{k}) = 1

(2)

\mathbf{r} \cdot (2\hat{i} - 7\hat{j} - 13\hat{k}) = 1

(3)

\mathbf{r} \cdot (2\hat{i} + 7\hat{j} + 13\hat{k}) = 0

(4) None of these