Question
Let the acute angle bisector of the two planes x-2 y-2 z+1=0 and 2 x-3 y-6 z+1=0 be the plane P. Then which of the following points lies on P?
BITSAT
Mathematics
Three Dimensional Geometry
2024
BITSAT 2024 (Memory Based Paper 2)
BITSAT Mathematics Question (2024) — Solution
Options
- A. (3,1,- 1 2 )
- B. (-2,0,- 1 2 )
- C. (0,2,-4)
- D. (4,0,-2)
Answer
B. (-2,0,- 1 2 )
Step-by-step solution
Given that P_1: x-2 y-2 z+1=0 P_2: 2 x-3 y-6 z+1=0 Equation of plane bisectors aligned & | x-2 y-2 z+1 1+4+4 |= | 2 x-3 y-6 z+1 2^2+3^2+6^2 | \\ & x-2 y-2 z+1 3 = 2 x-3 y-6 z+1 7 aligned Since a _1 a _2+ b _1 ~b _2+ c _1 c _2=20 0 Negative sign will be taken for acute bisector. aligned & 7 x-14 y-14 z+7=-[6 x-9 y-18 z+3] \\ & 13 x-23 y-32 z+10=0 \\ & (-2,0,- 1 2 ) satisfy it aligned
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks