Answer
a) $z $ ; b) $x$; c) $y$
Work Step by Step
a) The distance between two points can be calculated as: $\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$
Here, the distance from point $P(x,y,z)$ to the xy-plane, that is, $(x,y,0)$ is given by
$\sqrt{(x-x)^2+(y-y)^2+(z-0)^2}=\sqrt{z^2}=z$
b) The distance between two points can be calculated as: $\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$
Here, the distance from point $P(x,y,z)$ to the yz-plane, that is, $(0,y,z)$ is given by
$\sqrt{(x-0)^2+(y-y)^2+(z-z)^2}=\sqrt{x^2}=x$
c) The distance between two points can be calculated as: $\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}$
Here, the distance from point $P(x,y,z)$ to the zx-plane, that is, $(x,0,z)$ is given by
$\sqrt{(x-x)^2+(y-0)^2+(z-z)^2}=\sqrt{y^2}=y$
Hence, a) $z $ ; b) $x$; c) $y$
