Question

The radius of the sphere $|\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3$ is

• A. $2$
• B. $3$
• C. $1$
• D. $9$

Answer 1

Answer: (C)

$1$

Answer 2

Given, sphere is $|3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k})|=3$
$\Rightarrow$ $3\left| \vec{r}-\left( -\frac{2}{3}\hat{i}+\frac{1}{3}\hat{j}+\frac{4}{3}\hat{k} \right) \right|=3$
$\Rightarrow$ $\left| \vec{r}-\left( -\frac{2}{3}\hat{i}+\frac{1}{3}\hat{j}+\frac{4}{3}\hat{k} \right) \right|=1$