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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

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

Answers (1)

Given, xy + yz = 0

                                    => x (y + z) = 0

                                    => x = 0 and y + z = 0

Clearly, the above equations are the equations of planes [of the form ax + by + cz + d = 0]

Also, x = 0 has the normal vector  \hat{i}

And y + z = 0 has the normal vector  \hat{j}+\hat{k}

And the dot product of these two is

\hat{i}\left (\hat{j}+\hat{k} \right )=\hat{i}.\hat{j}+\hat{i}.\hat{k}

= 0

Hence, the planes are perpendicular (Option D).

Posted by

infoexpert24

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