An electric charge \(10^{-6} \, \mu C\) is placed at the origin (0, 0) of an X-Y coordinate system. Two points P and Q are situated at \((\sqrt{3}, \sqrt{3}) \, \text{mm}\) and \((\sqrt{6}, 0) \, \text{mm}\) respectively. The potential difference between the points P and Q will be:
Let \( \vec{a} = 3\hat{i} + \hat{j} - 2\hat{k} \), \( \vec{b} = 4\hat{i} + \hat{j} + 7\hat{k} \), and \( \vec{c} = \hat{i} - 3\hat{j} + 4\hat{k} \) be three vectors.
If a vector \( \vec{p} \) satisfies \( \vec{p} \times \vec{b} = \vec{c} \times \vec{b} \) and \( \vec{p} \cdot \vec{a} = 0 \), then \( \vec{p} \cdot (\hat{i} - \hat{j} - \hat{k}) \) is equal to