Question

Find the equation of the planes passing through the lines 2x – y + z = 3, 3x + y + z = 5 and which at a distance of 1/√6 from the point (2, 1, –1).

Answer 1

The equation of the plane passing through the line of intersection

2x – y + z = 3, 3x + y + z = 5 is 

in Eq. (i), we get the required equations of the planes are

2x – y + z = 3

or 62x + 29y + 19z – 105 = 0