3D Geometry
Three Dimensional Geometry
star_batch_jee_advanced_2025
Grade 12
Question:
The equation of planes bisecting the angle between the planes $2x - y + 2z + 3 = 0$ and $3x - 2y + 6z + 8 = 0$ is/are:
5x - y - 4z - 45 = 0
5x - y - 4z - 3 = 0
23x - 13y + 32z + 45 = 0
23x - 13y + 32z + 5 = 0
Step-by-Step Solution
Key Concept: Angle bisectors between two planes are obtained by equating the normalized distances with both signs.
The angle bisectors between planes $2x - y + 2z + 3 = 0$ and $3x - 2y + 6z + 8 = 0$ are found using $\frac{2x - y + 2z + 3}{\sqrt{4 + 1 + 4}} = \pm\frac{3x - 2y + 6z + 8}{\sqrt{9 + 4 + 36}}$. This gives the two bisecting planes $5x - y - 4z - 3 = 0$ and $23x - 13y + 32z + 45 = 0$.
Correct Answer: 2,3