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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`

Text Solution

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`L_1 = (x-1)/2 = (y+1)/2 = (z-1)/4 `; passes from (1,-1,1)
`L_2 = (x-3)/1 = (y-k)/2 = z/1` ; passes from (3,k,0)
`L_1 & L_2` are in same plane
`Dr's of L_1 = (2,2,4)`
`Dr's of L_2 = (1,2,1)`
line `L_3 ` passes from (1,-1,1) & (3, k ,0)
`Dr's of L_3 = (2, k+1, -1)`
`L_1, L_2, L_3 `are coplanar
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