Question:
The radius of the sphere $ |\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3 $ is
The radius of the sphere $ |\,3\,\vec{r}+2\hat{i}-\hat{j}-4\hat{k}|=3 $ is
Updated On: Jun 23, 2024
- $ 2 $
- $ 3 $
- $ 1 $
- $ 9 $
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The Correct Option is C
Solution and Explanation
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 $
$ \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 $
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