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Question:

A symmetrical form of the line of intersection of the planes x = ay + b and z = cy + d is:

x−b−ab=y=z−d−cd

x−ab=y=z−cd

x−b−aa=y=z−d−cc

x−ba=y=z−dc

Solution:

x−ay−b=0(1)⇒y=x−ba−cy+z−d=0(2)Solving (1) and (2), we get cx=az−ad+bc. ⇒x=az−ad+bccSo, x−ba=y1=z−dcx−b−aa=y=z−d−cc