Question

Find the vector equation of the sphere with centre $(\hat{i}+2\hat{j}-3\hat{k})$ and radius $5$ units.

Answer 1

Radius $a=5$ and centre of sphere $\overrightarrow{c}=(\hat{i}+2\hat{j}-3\hat{k})$
We know that the equation to the sphere
$|\overrightarrow{r}.\overrightarrow{c}|=a$
$|\overrightarrow{r}-(\hat{i}+2\hat{j}-3\hat{k})|=5$