A) \[|\vec{r}-(\hat{i}+\hat{k})|=4\]
B) \[|\vec{r}+(\hat{i}+\hat{k})|={{4}^{2}}\]
C) \[\vec{r}(\hat{i}+\hat{k})=4\]
D) \[\vec{r}(\hat{i}+\hat{k})={{4}^{2}}\]
Correct Answer: A
Solution :
Given, centre of sphere \[=(1,0,1)\] and radius \[=4.\] \[\therefore \] Vector equation of sphere is\[|\vec{r}-\vec{a}|=R\] and centre of sphere in vector form \[=\hat{i}+0\hat{j}+\hat{k}\] \[=\hat{i}+\hat{k}\] Hence, the vector equation of sphere is \[|\hat{r}-(\hat{i}+\hat{k})|=4.\]
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