Name the octant in which each of the following points lies.
(i) $(1,2,3$)
(ii) $(4,-2,3)$
(iii) $(4,-2,-5)$
(iv) $(4,2,-5)$
(v) $(-4,2,5)$
(iv) $(-3,-1,6)$
(vii) $(2,-4,-7)$
(viii) $(-4,2,-5)$.
(i) Point $(1,2,3)$ lies in first quadrant.
(ii) $(4,-2,3)$ in fourth octant.
(iii) $(4,-2,-5)$ in eight octant.
(iv) $(4,2,-5)$ in fifth octant.
(v) $(-4,2,5)$ in second octant.
(vi) $(-3,-1,6)$ in third octant.
(vii) $(2,-4,-7)$ in eight octant.
(viii) $(-4,2,-5)$ in sixth octant.
If $A, B, C$ be the feet of perpendiculars from a point $P$ on the $X, Y$ and $Z$-axes respectively, then find the coordinates of $A, B$ and $C$ in each of the following where the point $P$ is
(i) $\mathrm{A}(3,4,2)$
(ii) $B(-5,3,7)$
(iii) $C(4,-3,-5)$
The coordinates of $A, B$ and $C$ are the following
(i) $A(3,0,0), B(0,4,0), C(0,0,2)$
(ii) $A(-5,0,0), B(0,3,0), C(0,0,7)$
(iii) $A(4,0,0), B(0,-3,0), C(0,0,-5)$
If $A, B$, and $C$ be the feet of perpendiculars from a point $P$ on the $X Y, Y Z$ and $Z X$-planes respectively, then find the coordinates of $A, B$ and $C$ in each of the following where the point $P$ is
(i) $(3,4,5)$
(ii) $(-5,3,7)$
(iii) $(4,-3,-5)$
We know that, on $X Y$-plane $z=0$, on $Y Z$-plane, $x=0$ and on $Z X$-plane, $y=0$. Thus, the coordinate of $A, B$ and $C$ are following
(i) $A(3,4,0), B(0,4,5), C(3,0,5)$
(ii) $A(-5,3,0), B(0,3,7), C(-5,0,7)$
(iii) $A(4,-3,0), B(0,-3,-5), C(4,0,-5)$
How far apart are the points $(2,0,0)$ and $(-3,0,0)$ ?
$$ \begin{aligned} &\text { Given points, } A(2,0,0) \text { and } B(-3,0,0)\\ &A B=\sqrt{(2+3)^2+0^2+0^2}=5 \end{aligned}$$
6 Find the distance from the origin to $(6,6,7)$.
Distance from origin to the point $(6,6,7)$
$$\begin{aligned} & =\sqrt{(0-6)^2+(0-6)^2+(0-7)^2} \quad\left[\because d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^2}\right] \\ & =\sqrt{36+36+49} \\ & =\sqrt{121}=11 \end{aligned}$$