Question
The shortest distance between the lines x-3 2 = y-2 3 = z-1 -1 and x+3 2 = y-6 1 = z-5 3 is :
BITSAT
Mathematics
Three Dimensional Geometry
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. 18 5
- B. 22 3 5
- C. 46 3 5
- D. 6 3
Answer
A. 18 5
Step-by-step solution
Give lines are x-3 2 = y-2 3 = z-1 -1 and x+3 2 = y-6 1 = z-5 3 Lines passes through the points a _1=(3,2,1) and a _2=(-3,6,5) , b _1=2 i +3 j - k b _1=2 i + j -3 k , a _2- a _1=6 i -4 j-4 k Shortest distance = | ( a _2- a _1 ) ( b _1 b _2 ) | | ( b _1 b _2 ) | b _1 b _2= | array ccc i & j & k \\ 2 & 3 & -1 \\ 2 & 1 & 3 array |=10 i -8 j -4 k ( a _2- a _1 ) ( b _1 b _2 )=60+32+16=108 | b _1 b _2 |= 100+64+16 = 180 S . D= 108 180 = 108 6 5 = 18 5
Related: Mathematics — Three Dimensional Geometry · All PYQ Banks