As the prelims examinations draw really close, many students were asking me to give questions to test their concepts for several topics. In class, I had the opportunity to explore several applications questions too. We saw several physics concepts mixed. We also have some conceptual questions that need students to be able to use the entire topic to solve it.

So I’ll share one here. This involves several concepts put together. I’ll put the solution up once I find the time. Concepts that will be involved, will be

1. Vector Product
2. Equations of Plane
3. Finding foot of perpendicular of point

The question in one a reflection of a plane in another plane. I think such questions will come out in a few guided steps in exams. But should a student be able to solve it independently, it shows that he has good understanding.

The plane $p$ has equation $x + y + z = 9$ and the plane $p_1$ contains the lines passing through $(0, 2, 3)$ and are parallel to $(1, -1, 0)$ and $(0, 1, 1)$ respectively. Find, in scalar product form, the equation of the plane which is the reflection of $p_1$ in $p$.