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

the lines `(x-2)/1` = `(y-3)/1` = `(z-4)/-k` and `(x-1)/k` = `(y-4)/1` = `(z-5)/1` are coplanar if k=?

Text Solution

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Coordinates of line 1 are `(2,3,4)` and its direction ratios are `(1,1,-k)`.
Coordinates of line 1 are `(1,4,5)` and its direction ratios are `(k,1,1)`.
These two lines will be coplanar if,
`|[1-2,4-3,5-4],[1,1,-k],[k,1,1]| = 0`
`=>|[-1,1,1],[1,1,-k],[k,1,1]| = 0`
`=>[-1(1+k) -1(1+k^2)+1(1-k)] = 0`
`=>-1-k-1-k^2+1-k = 0`
`=>k^2+2k+1 = 0`
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