Finding equation of plane

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Could anyone please tell me a relatively short approach on how to find equation of a plane if I'm given it is at equal distance from 2 given lines.... I tried finding the the equation of the line perpendicular to both the lines and hence the corresponding points on the both the lines and then using distance formula to equate the distance of a point (x, y, z) from both the points and then simplifying it... But I find the method(I'm not even sure if it's correct) very very long.. So it would be really helpful if anyone could suggest a short method for this one..