Question

The radius of the circular section of the sphere $|\overline{r}|=5$ by the plane $\overline{r}$. $(\hat{i}+\hat{j}+\hat{k})=3\sqrt{3}$ is:

• A. $2$
• B. $3$
• C. $2\sqrt{3}$
• D. $4$

Answer 1

The correct option is D $4$

$\overrightarrow{r}.(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k})=3\sqrt{3}$ is the plane $x+y+z=3\sqrt{3}$
The perpendicular distance of plane from $(0,0,0)$ is $\frac{|0+0+0-3\sqrt{3}|}{\sqrt{3}}=3$
The radius of given sphere is $5$.
Hence, the radius of generated circle is $r=\sqrt{5^2-3^2}=\sqrt{16}=4$.