Answer
a) $\sqrt{y^2+z^2}$; b) $\sqrt{x^2+z^2}$ c) $\sqrt{x^2+y^2}$
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 x-axis, that is, $(x,0,0)$ is given by
$\sqrt{(x-x)^2+(y-0)^2+(z-0)^2}=\sqrt{y^2+z^2}$
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 y-axis, that is, $(0,y,0)$ is given by
$\sqrt{(x-0)^2+(y-y)^2+(z-0)^2}=\sqrt{x^2+z^2}$
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 z-axis, that is, $(0,0,z)$ is given by
$\sqrt{(x-0)^2+(y-0)^2+(z-z)^2}=\sqrt{x^2+y^2}$
