Coordinate Axes and Coordinate Planes in 3D

Find the coordinates of the midpoint, $M$, of the diagonal $\left[AO\right]$ of the cuboid.

Write down the coordinates of point $A$ for the following cuboid:

Write down the coordinates of point $B$ for the following cuboid:

The equation of the locus of a point $P\left(x, y, z\right)$ such that it's distance from the $x$-axis is equal to its distance from the plane $x+z=1$ is

if the points $(1,1, \lambda )$ and $(-3,0,1)$ are equidistant from the plane $\overrightarrow{r}.\left(3\hat{i}+4\hat{j}-12\hat{k}\right)+13=0$, find the value of $\lambda$.

If the distance of the point $\hat{i}+2\hat{j}-\hat{k}$ from the plane $\overrightarrow{r}·\left(\hat{i}-2\hat{j}+4\hat{k}\right)=10$ is $\frac{17}{\sqrt{k}}$, then the find the value of $k$.

If the coordinate of the foot of the perpendicular from the point $(1,2,3)$ on $y$-axis is $(a,b,c)$ then find the value of $a+b+c$.

Write the distance of the point $P(2,3,5)$ from the $xy$ plane.

If the point $(-7,2-5)$ lie in $P^{\mathrm{th}}$ octant, then find the value of $P$.

If the point $(2,-5,-7)$ in $Q^{\mathrm{th}}$ octant, the find the value of $Q$

If the point $(-5,-3,-2)$ lie in $k^{\mathrm{th}}$ octant, then find the value of $k.$

If the point $(-5,-4,7)$ lie in $Q^{\mathrm{th}}$ octant, then find the value of $Q$.

Name the octant (First/Second/Third/Fourth/Fifth/Sixth/Seventh/Eighth) in which each of the following points lies.$(-3,-1,6)$.

A line is parallel to $x$-axis if all the points on the line have equal _____.

The equation of $z$-axis, are $x=0 \mathrm{and}$ _____.

To locate a place on a map two essential parameters are required, Latitude and Longitudinal Values of that point.

"The Global Positioning System works on the basic principles of Co-ordinate Geometry".

The distance between two points $P$ and $Q$ is $d$ and the length of the projections of $PQ$ on the co-ordinate planes are $d_1, d_2, d_3$. Then $d_1^2+d_2^2+d_3^2=k{d}^2$ where $k$ is

If a plane cuts off intercepts $OA=a,OB=b,\mathrm{ }OC=c$ from the co-ordinate axes, then the area of the triangle $ABC=$

The shortest distance of the point $\left(a,\mathrm{ }b,\mathrm{ }c\right)$ from the $x$ -axis is