Question
If the straight lines x-1 k = y-2 2 = z-3 3 and x-2 3 = y-3 k = z-1 2 intersect at a point, then the integer k is equal to
BITSAT
Mathematics
Three Dimensional Geometry
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. -5
- B. 5
- C. 2
- D. -2
Answer
A. -5
Step-by-step solution
When the two lines intersect then shortes distance between them is zero i.e. aligned & ( a _2- a _1 ) b _1 b _2 | b _1 b _2 | =0 \\ & ( a _2- a _1 ) b _1 b _2=0 aligned where a _1= i +2 j +3 k , b _1=k i +2 j +3 k aligned & a _2=2 i +3 j + k , b _2=3 i +k j +2 k \\ & | array ccc 1 & 1 & -2 \\ k & 2 & 3 \\ 3 & k & 2 array |=0 \\ & 1(4-3 k)-1(2 k-9)-2 (k^2-6 )=0 \\ & -2 k^2-5 k+25=0 k=-5 or 5 2 aligned
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks