Let the intercept made by the line x/1=y...

Let the intercept made by the line `x/1=y/2=z/3` between the plane x+y+z=3 and the line `[x-1]/2=[y-2]/-1=[z-3]/-1` is `lambda`, then `[4lambda]/sqrt[14]` is

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`x/1=y/2=z/3=k`
`x=k,y=2k,z=3k`
`A(k,2k,3k)`
`k+2k+3k=3`
`k=1/2`
`A=(1/2,1,3/2)`
`(k-1)/2=(2k-2)/-1=(3k-3)/-1`
`-k+1=4k-4`
...

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