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Show that the lines (x-1)/1 = (y-1)/(-2)...

Show that the lines `(x-1)/1 = (y-1)/(-2)=(z-1)/1 and (x-2)/5 = (y+1)/1 = (z-2)/(-6)` are coplanar.

Text Solution

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The lines
`(x-x_(1))/l_(1)=(y-y_(1))/m_(1) = (z-z_(1))/n_(1) and (x-x_(2))/l_(2)=(y-y_(2))/m_(2) = (z-z_(2))/n_(2)` are coplanar if
`abs[[x_(2)-x_(1),y_(2)-y_(2),z_(2)-z_(1)],[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)]]=0`
Substituting the values
`abs[[1-2,1-(-1),1-2],[1,-2,1],[5,1,6]]= -1(-13)-2(1)-1(11)`
`= 0` So lines are coplanar.
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