Question

A parallelopiped is formed by planes drawn through the points $(1,2,3)$ and $(9,8,5)$ parallel to the coordinate planes then which of the following is not the length of an edge of this rectangular parallelopiped

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is B $4$

Given Points $A(1,2,3)$ and $B(9,8,5)$

eq of plane from point A(1,2,3)

$a(x-1)+b(y-2)+c(z-3)=0$-----------(1)

eq is also parallel to $x=0,y=0,z=0$

when $x=0$ from eq (1) we get

$x-1=0$ it is the plane of parallelopiped so length of edge is the distance from point B(9,8,5)

$\Rightarrow distance=\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}$

$\Rightarrow distance=\frac{1\left(9\right)-1}{\sqrt{1^2}}$

$\Rightarrow distance=8$

now plane is parallel to $y=0$ for other plane of parallelopid

$y-2=0$

distance from point B=length of edge

$\Rightarrow distance=\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}$

$\Rightarrow distance=\frac{1\left(8\right)-2}{\sqrt{1^2}}$

$\Rightarrow distance=6$

now plane is parallel to $z=0$ for another plane of parallelopid

$z-3=0$

distance from point B=length of edge

$\Rightarrow distance=\frac{a{x}_1+b{y}_1+c{z}_1+d}{\sqrt{a^2+b^2+c^2}}$

$\Rightarrow distance=\frac{1\left(5\right)-3}{\sqrt{1^2}}$

$\Rightarrow distance=2$

length of edges are $2,6,8$