Question

If the distance between planes $4x-2y-4z+1=0$ and $4x-2y-4z+d=0$ is $7$, then $d$ is :

• A. $41$ or $-42$
• B. $42$ or $-43$
• C. $-41$ or $43$
• D. $-42$ or $44$

Answer 1

Answer: (C)

$-41$ or $43$

Distance between two planes $4x-2y-4z+1=0$ and $4x-2y-4z+d=0$ is given by

$D=\frac{|1-d|}{\sqrt{{\left(4\right)}^2+{(-2)}^2+{(-4)}^2}}$

$⟹7=\frac{|1-d|}{6}$

$⟹1-d=\pm 42$

$⟹d=-41$ or $43$