The locus represented by xy + yz = 0 is


Given, xy + yz = 0


x(y + z) = 0


x = 0 and y + z = 0


Clearly, above equations are equation of planes [As they have form Ax + By + Cz + D = 0 form]


Also, x = 0 has normal vector


And y + z = 0 has normal vector


And dot product of these two is



= 0 + 0


= 0


Hence, planes are perpendicular [As the dot product of normal of two perpendicular planes is 0]

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