Given equation of planes are
x−2y−z+5=0 and
x+y+3z=6 Firstly, determine the intersection lines of two planes.
Let the DR's of intersection line are
a,b and
c since, the normal to the given planes are perpendicular to the intersecting line.
∴a(1)+b(−2)+c(−1)=0 ⇒a−2b−c=0....(i)
and
a(1)+b(1)+c(3)=0 ⇒a+b+3c=0....(ii)
From Eqs. (i) and (ii), we get
== == since, the required line is passing through (2,3,1) and parallel to the line of intersection.
∴==