Question

The perpendicular distance from origin to plane $F.(3,4,12)=65$ is _______

• A. $1$
• B. $5$
• C. $13$
• D. $65$

Answer 1

The correct option is B $5$

$\to \overline{r}.(3,4,12)=65$
$\therefore (x,y,z).(3,4,12)=65$
$\therefore$ perpendicular distance from origin to the plane is $p=\frac{\left|c\right|}{\sqrt{a^2+b^2+c^2}}$
$\therefore p=\frac{|-65|}{\sqrt{9+16+144}}=\frac{65}{13}=5$