Question

A vector parallel to the line of intersection of the planes \[ \overrightarrow{r} \cdot (3\hat{i} - \hat{j} + \hat{k}) = 1 \quad \text{and} \quad \overrightarrow{r} \cdot (\hat{i} + 4\hat{j} - 2\hat{k}) = 2 \] is:

• A. \( -2\hat{i} + 7\hat{j} + 13\hat{k} \)
• B. \( 2\hat{i} - 7\hat{j} + 13\hat{k} \)
• C. \( -\hat{i} + 4\hat{j} + 7\hat{k} \)
• D. \( \hat{i} - 4\hat{j} + 7\hat{k} \)

Hint:

To find the direction vector of the line of intersection of two planes, calculate the cross product of their normal vectors: \( \overrightarrow{n_1} \times \overrightarrow{n_2} \).