Question
The lines x-2 1 = y-3 1 = z-4 -k and x-1 k = y-4 2 = z-5 1 are coplanar if
BITSAT
Mathematics
Three Dimensional Geometry
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. k =3 or -2
- B. k =0 or -1
- C. k =1 or -1
- D. k =0 or -3
Answer
D. k =0 or -3
Step-by-step solution
Two planes are coplanar if | array ccc x_2-x_1 & y_2-y_1 & z_2-z_1 \\ l_1 & m_1 & n_1 \\ l_2 & m_2 & n_2 array |=0 | array ccc 1 & -1 & -1 \\ 1 & 1 & -k \\ k & 2 & 1 array |=0 Applying C _2 C _2+ C _1, C _3 C _3+ C _1 | array ccc 1 & 0 & 0 \\ 1 & 2 & 1-k \\ k & k+2 & 1+k array |=0 1[2+2 k-(k+2)(1-k)]=0 2+2 k- (-k^2-k+2 )=0 k^2+3 k=0 k(k+3)=0
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks