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Question

Find the shortest distance between two lines : x12=y23=z34 and x23=y44=z55 is

A
16
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B
16
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C
136
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D
13
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Solution

The correct option is B 16
Given lines
l1:x12=y23=z34
l2:x23=y44=z55
position vector of line l1
a=^i+2^j+3^k
position vector of line l2
c=2^i+4^j+5^k
normal vector of line l1
n1=2^i+3^j+4^k
normal vector of line l2
n2=3^i+4^j+5^k
so line are skews line
SD=(ca)(n1×n2)|(n1×n2)|
ca=2^i+4^j+5^k^i2^j3^k
ca=^i+2^j+2^k
n1×n2=∣ ∣ ∣^i^j^k234345∣ ∣ ∣
n1×n2=^i(1516)^j(1012)+^k(89)

n1×n2=^i+2^j^k
|n1×n2|=(12)+22+(1)2

|n1×n2|=6
putting ca,n1×n2,|n1×n2| in formula

SD=∣ ∣(^i+2^j+2^k)(^i+2^j^k6∣ ∣

SD=1+426

SD=16

SD=16


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