When an equation of line is given as intersection of two planes like $$ax + by + cz + d = 0 = px + qy + rz + s,$$ why do we put $z=0$?
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2Maybe because $z$ serves as a parameter, that is, $z=t$ for any real number $t$, in particular, we can take $z=0$. – Juniven Acapulco Apr 30 '17 at 04:51