Question
The shortest distance between the lines x = y + 2=6 z-6 and x+1=2 y=-12 z is
BITSAT
Mathematics
Three Dimensional Geometry
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. 1 2
- B. 2
- C. 1
- D. 3 2
Answer
B. 2
Step-by-step solution
The lines are x 6 = y+2 6 = z-1 1 and x+1 12 = y 6 = z -1 Here, aligned & a _1=-2 j + k , b_1+6 i +6 j + k , a _2=- i , \\ & b _2=12 i +6 j - k \\ & b _1 b _2= | array ccc i & j & k \\ 6 & 6 & 1 \\ 12 & 6 & -1 array |=-12 i +18 j -36 k \\ & Shortest distance = | ( a _2- a _1 ) ( b _1- b _2 ) | | b _1 b _2 | aligned aligned & = |(- i +2 j - k ) (-12 i+18 j -36 k )| (-12)^2+(18)^2+(-36)^2 \\ & = |+12+36+36| 1764 = 84 42 =2 aligned
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks