Fill in the blanks

The equation of z-axis, are ________.

x = 0, y = 0.

Explanation:

Let P be an arbitrary point on z-axis. Its locus will give the equation of z - axis

∵ P lies on z-axis and this axis is common to xz and yz planes or we can say that it lies on xz and yz planes.

∴ it’s y and x coordinates are going to be 0 but still it may have any distance form xy axis as it is ⊥ to it.

∴ Co-ordinates of P are of the form (0, 0, z)

Clearly x = 0 and y = 0 together defines any point on z – axis.

∴ locus of P is x = 0 & y = 0 and also the equation of z-axis.