Question

The locus of a point $P(x,y,z)$ which moves in such a way that $z=c\left(constant\right)$, is a:

• A. line parallel to z- axis
• B. plane parallel to xy- plane
• C. line parallel to y- axis
• D. line parallel to x- axis

Answer 1

The correct option is B plane parallel to xy- plane

At time $t=0$ let the locus point be $(x_1,y_1,z_1)$

At $t=t^{\prime }$ the point be $(x_2,y_2,z_1)$ .... since the point is moving with a constant z coordinate. That is, the locus of the point or the particle is such that it has zero displacement in the z direction.

Now

$P_{t^{\prime }}-P_0$
$=(x_2-x_1)i+(y_2-y_1)j+0k$

Hence the locus of the point is in the plane parallel to xy-plane.