3D Geometry
Three Dimensional Geometry
star_batch_jee_advanced_2025
Grade 12
Question:
If $abc \neq 0$ and let $(p_1, q_1, r_1)$ be the image of $(p, q, r)$ in the plane $ax + by + cz + d = 0$, then:
$\frac{p_1-p}{a} = \frac{q_1-q}{b} = \frac{r_1-r}{c}$
$a(p + p_1) + b(q + q_1) + c(r + r_1) + 2d = 0$
Both (A) and (B)
None of these
Step-by-Step Solution
Key Concept: Mirror reflection requires both that the midpoint lies on the mirror and that the connecting line is perpendicular to it.
For a plane mirror, the midpoint of the object and image lies on the mirror plane, and the line joining object and image is perpendicular to the mirror. Using these two conditions: the midpoint satisfies the mirror equation, and the direction vector of the object-image line is perpendicular to the mirror's normal vector.
Correct Answer: 3