K. C. Sinha and Abhishek Chandra Solutions for Exercise 1: EXERCISE

Let $A$, $B$, $C$ be the feet of perpendicular drawn from a point $P$ to $X$, $Y$ and $Z$-axis, respectively. Find the coordinates of $A$, $B$, $C$ if coordinates of $P$ are $(3,4,2)$.

Let $A$, $B$, $C$ be the feet of perpendicular drawn from a point to $X$, $Y$ and $Z$-axes, respectively. Find the coordinates of $A$, $B$, $C$ if coordinates of $P$ are $(3,-5,1)$.

Find the distance of point $(-1,-3,4)$ from $x$, $y$ and $z$-axes, respectively.

Find the distance between the points $\left(0,1,-3\right)$ and $\left(3,0,5\right)$.

If the origin is the centroid of $△ABC$ with vertices $A\left(\alpha ,1,3\right), B\left(-2,\beta ,-5\right)$ and $C\left(4,7,\gamma \right)$, then find the value of $\alpha$, $\beta$ and $\gamma$.

The origin is the centroid of the triangle $PQR$ with vertices $P\left(2a,2,6\right), Q\left(-4,3b,-10\right)$ and $R\left(8,14,2c\right)$. Find the values of $a$, $b$ and $c$.

The centroid of a triangle $ABC$ is at the point $G\left(1,1,1\right)$. If the coordinates of $A$ and $B$ are $\left(3,-5,7\right)$ and $\left(-1,7,-6\right)$, respectively, then find the coordinates of the point $C$.

Find the centroid of a triangle, the midpoints of whose sides are $\left(1,2,-3\right), \left(3,0,1\right)$ and $\left(-1,1,-4\right)$.