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Question

The distance between lines x+54=y+3āˆ’18=zāˆ’6āˆ’4 and xāˆ’32=y+10āˆ’9=zāˆ’1āˆ’2(approx.) is

A
6
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B
7.5
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C
8
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D
9
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Solution

The correct option is B 7.5
Given lines
x+54=y+318=z64-----(1)
x32=y+109=z12------(2)
on comparing both lines with general cartesian form
normal vector of line
b=2^i9^j2^k
position vector of line eq (1)
a=5^i3^j+6^k
position vector of line (2)
c=3^i10^j+^k
ca=3^i10^j+^k(5^i3^j+6^k)
ca=3^i10^j+^k+5^i+3^j6^k
ca=8^i7^j6^k
(ca)×b=∣ ∣ ∣^i^j^k876292∣ ∣ ∣
(ca)×b=^i(1454)^j(16+12)+^k(72+14)
(ca)×b=40^i+4^j58^k
formula to find distance between parallel lines
SD=(ca)×bb
SD=40^i+4^j58^k22+(9)2+(2)2
SD=(40)2+42+(58)24+81+4
SD=1600+16+336489
SD=498089
SD=55.95
SD=55.95
SD=7.5 approx


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