If $(b+c)x+(c+a)y+(a+b)z=k=(b-c)x+(c-a)y+(a-b)z$ then what will be the equation of the straight line passing through origin and parallel to given line ?

I tried to relate the direction ratios of the given line and the new line as they are parallel but the problem is that line is passing through origin so I am ending up getting all zeros. Please help. Any hint will do .

I tried to relate the direction ratios of the given line and the new line as they are parallel but the problem is that line is passing through origin so I am ending up getting all zeros. Please help. Any hint will do .