A line is parallel to $X$-axis, if all the points on the line have equal .............. .
$y$ and $z$-coordinates.
$x=a$ represent a plane parallel to .............. .
$x=$ a represent a plane parallel to $Y Z$-plane.
The plane parallel to YZ-plane is perpendicular to .................... .
The plane parallel to $Y Z$-plane is perpendicular to $X$-axis.
The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are ............. .
Given dimensions are $a=10, b=13$ and $c=8$.
$$\begin{aligned} \therefore \quad \text { Required length } & =\sqrt{a^2+b^2+c^2} \\ & =\sqrt{100+169+64}=\sqrt{333} \end{aligned}$$
If the distance between the points $(a, 2,1)$ and $(1,-1,1)$ is 5 , then $a$ ......... .
Given points are $(a, 2,1)$ and $(1,-1,1)$.
$$\begin{array}{lr} \therefore & \sqrt{(a-1)^2+(2+1)^2+(1-1)^2}=5 \\ \Rightarrow & (a-1)^2+9+0=25 \\ \Rightarrow & a^2-2 a+1+9=25 \\ \Rightarrow & a^2-2 a-15=0 \\ \Rightarrow & a^2-5 a+3 a-15=0 \\ \Rightarrow & a(a-5)+3(a-5)=0 \\ \Rightarrow & (a-5)(a+3)=0 \\ \Rightarrow & a-5=0 \text { or } a+3=0 \\ \therefore & a=+5 \text { or }-3 \end{array}$$