
Which of the points $P\left(6,2,3\right)$,
$Q\left(5,1,4\right)$, and $R\left(0,3,8\right)$ is closest to the
$xz\text{plane}$? Which point lies in the $yz\text{plane}$?
$Q$; $R$.
Describe and sketch a surface in ${\mathbb{R}}^{3}$ represented by the equation $x+y=2$.
A vertical plane that intersects the
$xy\text{plane}$ in the line $y=2x$, $z=0$.
Find an equation of the sphere with
center $\left(2,6,4\right)$ and radius $5$. Describe its
intersection with each of the coordinate planes.
${\left(x2\right)}^{2}+{\left(y+6\right)}^{2}+{\left(z4\right)}^{2}=25$
circle of radius $3$ for $z=0$, circle of radius
$\sqrt{21}$ for $x=0$, and empty set for $y=0$.
Show that the following equation is
that of a sphere, and find its center and
radius.
$4{x}^{2}+4{y}^{2}+4{z}^{2}8x+16y=1$
Find an equation of the sphere if one
of its diameters has endpoints $\left(2,1,4\right)$ and $\left(4,3,10\right)$.
Describe in words the region of ${\mathbb{R}}^{3}$ represented by the equation $y=4$.
A plane parallel to the $xz\text{plane}$ and $4$
units to the left of it.
Describe in words the region of ${\mathbb{R}}^{3}$ represented by the inequality ${x}^{2}+{y}^{2}+{z}^{2}>2z$.
Write inequalities describing the
solid upper hemisphere of the sphere of radius $2$ centered at
the origin.