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If the lines (x-1)/2=(y+1)/3=(z-1)/4a n ...

If the lines `(x-1)/2=(y+1)/3=(z-1)/4a n d(x-3)/1=(y-k)/2=z/1` intersect, then find the value of `kdot`

A

`(3)/(2)`

B

`(9)/(2)`

C

`-(2)/(9)`

D

`-(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given line are `(x-1)/2=(y+1)/3=(z-1)/(4)=lambda ` [say]
`and (x-3)/(1)=(y-k)/2=z/1=mu` [say]
`Rightarrow x=2lambda+1, y=3lambda-1, z=4lambda+1`
`and x=mu+3, y=2mu+k, z=mu` are same
Since the lines intersect, So, they must have a point in common, i.e,
`2lambda+1=mu+3, 3lambda-1=2mu+k, z=mu`
On solving 1st and III rd terms, we get
`lambda=-3/2 and mu=-5`
`therefore k=3lambda-2mu-1`
`Rightarrow k=3 (-(3)/2)-2(-5)-1=9/2`
`therefore k=9/2`
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