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Read the following passage and answer th...

Read the following passage and answer the questions. Consider the lines
`L_(1) : (x+1)/(3)=(y+2)/(1)=(z+1)/(2)`
`L_(2) : (x-2)/(1)=(y+2)/(2)=(z-3)/(3)`
Q. The shortest distance between `L_(1) and L_(2)` is

A

`1/(sqrt(99))(-hati+7hatj+7hatk)`

B

`1/(5sqrt(5))(-hati-7hatj+5hatk)`

C

`1/(5sqrt(3))(-hati+7hatj+5hatk)`

D

`1/(sqrt(99))(7hati-7hatj-hatk)`

Text Solution

Verified by Experts

The correct Answer is:
B
Lines `L_(1)` and `L_(2)` are parallel to the vectors `vecb_(1)=3hati+hatj+2hatk` and `vecb_(2)=hati+2hatj+3hatk` respectively.
Therefore, a unit vector perpendicular to both `L_(1)` and `L_(2)` is
`hatn=(vecb_(1)xxvecb_(2))/(|vecb_(1)xxvecb_(2)|)`
Now `vecb_(1)xxvecb_(2)=|(hati,hatj,hatk),(3,1,2),(1,2,3)|=-hati-7hatj+6hatk`
`:.hatn=1/(5sqrt(3))(-hati-7hatj+5hatk)`
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