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Question:

Find the distance between the planes2x−y+2z=5and5x−2;.5y+5z=20.Find the distance between the planes2x−y+2z=5and5x−2;.5y+5z=20.2x−y+2z=52x−y+2z=52x−y+2z=522xx−−yy++22zz==555x−2;.5y+5z=205x−2;.5y+5z=205x−2;.5y+5z=2055xx−−2;.52.5yy++55zz==2020?

Solution:

The distance between two parallel planes of the formax+by+cz=d1,ax+by+cz=d2is|d1−d2|√a2+b2+c25x−2;.5y+5z=20On taking2.5common on both sides2.5(2x−y+2z)=2.5×8The second equation can be written as2x−y+2z=8⇒the distance between the given planes2x−y+2z=5and2x−y+2z=8is|8−5|√22+12+22=1