Question

The vector equation of sphere with centre having the position vector $3\hat{i}+\hat{j}-2\hat{k}$ and radius $9$ units is

• A. $\left|\vec{r}\cdot \left(3\hat{i}+\hat{j}+2\hat{k}\right)\right|=9$
• B. $\left|\vec{r}\cdot \left(3\hat{i}+\hat{j}-2\hat{k}\right)\right|=9$
• C. $\left|\vec{r}\cdot \left(3\hat{i}+\hat{j}-2\hat{k}\right)\right|=-9$
• D. None of these

Answer 1

Answer: (B)

Position vector of centre is $3\hat{i}+\hat{j}-2\hat{k}$,
radius = $9$ units = $R$
$\therefore$ Required equation is $\left|\vec{r}-\vec{c}\right|=R$
$\Rightarrow \left|\vec{r}-\left(3\hat{i}+\hat{j}-2\hat{k}\right)\right|=9$