Question

The vector equation of the sphere whose centre is the point (1, 0, 1) and radius is 4, is:

• 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. $\vec{r}(\hat{i}+\hat{k})=4^2$

Answer 1

Answer: (A)

Given, centre of sphere $=(1,0,1)$ and radius $=4$
$\therefore$ Vector equation of sphere is $|\overrightarrow{r}-\overrightarrow{a}|=R$ 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
$|\overrightarrow{r}-(\hat{i}+\hat{k})|=4$