Introduction to Three Dimensional Geometry

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Thegiven\text{\hspace{0.17em}points}are\left(a,2,1\right)and\left(1,-1,1\right)\\ \therefore \text{\hspace{0.17em}Distance}=\sqrt[]{{\left(a-1\right)}^2+{\left(2+1\right)}^2+{\left(1-1\right)}^2}\\ 5=\sqrt[]{a^2+1-2a+9}\\ Squaringbothsides,wehave\\ 25=a^2+1-2a+9\\ \Rightarrow a^2-2a-15=0\\ \Rightarrow a^2-5a+3a-15=0\\ \Rightarrow a\left(a-5\right)+3\left(a-5\right)=0\\ \Rightarrow \left(a+3\right)\left(a-5\right)=0\\ \therefore a=-3or5\\ Hence,thevalueofthefilleris5or-3.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$Thegiven\text{\hspace{0.17em}dimensions}$
$\begin{array}{l}are10,13and8\\ Leta=10,b=13andc=8\\ \therefore \text{\hspace{0.17em}Required}length=\sqrt[]{a^2+b^2+c^2}\\ =\sqrt[]{{\left(10\right)}^2+{\left(13\right)}^2+{\left(8\right)}^2}=\sqrt[]{100+169+64}=\sqrt[]{333}\\ Hence,thevalueofthefilleris\sqrt[]{333}.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Theplaneparalleltoyz-planeisperpendiculartox-axis.\\ Hence,thevalueofthefillerisx-axis.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$x=arepresentsaplaneparalleltoyz-plane.$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}yandzcoordinates.\\ Hence,thevalueofthefillerisyandzcoordinates.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}z-coordinates.\\ Hence,thevalueofthefillerisz-coordinates.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Theequationofz-axisare,x=0andy=0.\\ Hence,thevalueofthefillerisx=0andy=0.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Onthez-axis,x=0andy=0.\\ \therefore Therequiredcoordinateisintheformof\left(0,0,z\right).\\ Hence,thevalueofthefilleris\left(0,0,z\right).\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Theequationofyz-planeisx=0.\\ Hence,thevalueofthefillerisx=0.\end{array}$

This is a Fill in the blanks Type Questions as classified in NCERT Exemplar

$\begin{array}{l}Weknowthatyzplane,x=0\\ So,thecoordinatesoftherequired\text{\hspace{0.17em}point}is\left(0,y,z\right).\\ Hence,thevalueofthefilleris\left(0,y,z\right).\end{array}$