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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`

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`(x-1)/(2)=(y+1)/(3)=(z-1)/(4)= lamda`
`rArr" "x=2lamda+1, y=3lamda-1 and z=4lamda+1`.
`" "(x-3)/(1)=(y-k)/(2)=(z)/(1)=mu`
`rArr" "x=3+mu, y=k+2mu and z=mu`.
Since the above lines intersect, we have
`" "2lamda+1=3+mu" "`(i)
`" "3lamda-1=2mu+k" "` (ii)
`" "mu=4lamda+1" "`(iii)
Solving (i) and (iii) and putting the value of `lamda and mu` in (ii), `k=9//2`.
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