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if the lines (x-1)/2=(y-1)/3=(z-1)/4 and...

if the lines `(x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1` intersect then the value of `k` is (a) `1/3` (b) `2/3` (c) `-1/3` (d) `1`

A

`(3)/(2)`

B

`(9)/(2)`

C

`-(2)/(9)`

D

`-(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, the lines intersect, therefore they must have a point in common, i.e.
`(x-1)/(2)=(y+1)/(3)=(z-1)/(4)=lambeda`
and`" "(x-3)/(1)=(y-k)/(2)=(z)/(1)=mu`
`implies" "x=2lambda+1,y=3lambda-1`
`z=4lambda+1`
and`" "x=mu+3,y=2mu+k,z=mu` are same.
`implies" "2lambda+1=mu+3`
`3lambda-1=2mu+k`
`4lambda+1=mu`
On solving Ist and IIIrd terms, we get,
`lambda=-(3)/(2)" and "mu=-5`
`:." "k=3lambda-2mu-1`
`implies" "k=3(-(3)/(2))-2(-5)-1=(9)/(2)`
`:." "k=(9)/(2)`
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