The locus represented by xy + yz = 0 is
(a) a pair of perpendicular lines
(b) a pair of parallel lines
(c) a pair of parallel planes
(d) a pair of perpendicular planes

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Solution

Given xy + yz = 0
i.e. (x + z)y = 0
i.e. x + z = 0 or y = 0
Which represent two plane
For plane y = 0, normal is $\hat{j}$ and normal to plane x + z = 0 is $\hat{i} + \hat{k}$
Since ( $\hat{i} + \hat{k}$ ). $\hat{j}$ =0
⇒ Two planes are perpendicular (∵ normals are perpendicular)

Hence, the correct answer is option D.

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The locus represented by xy + yz = 0 is (a) a pair of perpendicular lines (b) a pair of parallel lines (c) a pair of parallel planes (d) a pair of perpendicular planes

Given xy + yz = 0 i.e. (x + z)y = 0 i.e. x + z = 0 or y = 0 Which represent two plane For plane y = 0, normal is j^ and normal to plane x + z = 0 is i^+k^ Since (i^+k^).j^ =0 ⇒ Two planes are perpendicular (∵ normals are perpendicular) Hence, the correct answer is option D.

The locus represented by xy + yz = 0 is
(a) a pair of perpendicular lines
(b) a pair of parallel lines
(c) a pair of parallel planes
(d) a pair of perpendicular planes