Question

Find the distance between the point \(2\hat{i} + \hat{j} - \hat{k}\) and the plane \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 9\).

• A. \(\frac{13}{\sqrt{21}}\)
• B. \(\frac{9}{\sqrt{21}}\)
• C. \(\frac{13}{21}\)
• D. \(\frac{21}{\sqrt{13}}\)

Hint:

For point–plane distance problems, always treat the plane as \( \vec{r}\cdot \vec{n} - d = 0 \) to avoid sign mistakes in exams.

Answer 1

The Correct Option is A