Question

The distance between the planes $r\cdot (i+2j-2k)+5=0$ and $r\cdot (2i+4j-4k)-16=0$ is

• A. $3$
• B. $\frac{11}{3}$
• C. $13$
• D. $-13$
• E. $\frac{13}{3}$

Answer 1

The correct option is E $\frac{13}{3}$

Given equation of planes in vector form are
$r\cdot (i+2j-2k)+5=0$
and $r\cdot (2i+4j-4k)-16=0$
Equation of planes in cartesian form are
$x+2y-2z+5=0$ ..... (i)
and $2x+4y-4z-16=0$
or $x+2y-2z-8=0$ .... (ii)
We observe that both planes are parallel to each other.
Therefore, required distance is $\frac{|5+8|}{\sqrt{1+4+4}}=\frac{13}{3}$.