Question

The equation $|\overline{r}{|}^2-\overline{r}\cdot (2\hat{i}+4\hat{j}+4\hat{k})-16=0$ represent a

• A. a circle
• B. a sphere of radius 3 units
• C. a plane
• D. a sphere of radius 5 units

Answer 1

The correct option is D a sphere of radius 5 units

$|\overline{r}{|}^2-\overline{r}(2i+4j+4k)-16=0$
$|\overline{r}{|}^2-2\overline{r}(i+2j+2k)+|i^2+(2j{)}^2+(2k{)}^2|-9-16=0$
$(\overline{r}-(i+2j+2k){)}^2=25$
Clearly this is equation of a sphere with PV $i+2j+2k$ and radius $5$.