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
$|\overrightarrow{ r }-(\hat{ i }+\hat{ k })|=4$