Question

Let A be a point having position vector \( \vec{i}-3\vec{j} \) and \( \bar{r} = (\vec{i}-3\vec{j}) + t(\vec{j}-2\vec{k}) \) be a line. If P is a point on this line and is at a minimum distance from the plane \( \bar{r} \cdot (2\vec{i}+3\vec{j}+5\vec{k}) = 0 \), then the equation of the plane through P and perpendicular to AP is

• A. \( \bar{r} \cdot (-\vec{j}+2\vec{k}) = 8 \)
• B. \( \bar{r} \cdot (\vec{j}+\vec{k}) = 4 \)
• C. \( \bar{r} \cdot (\vec{i}+\vec{j}+\vec{k}) = 8 \)
• D. \( \bar{r} \cdot (\vec{i}-\vec{j}) = 12 \)

Hint:

Minimum distance from a line to a plane is zero if they intersect.

Answer 1

The Correct Option is A