Question

The equation of sphere with centre $(1,-2,3)$ and touching the planes $6x-3y+2z-4=0$ is

• A. $|\overline{r}-(\hat{i}-2\hat{j}+3\hat{k})|=2$
• B. $|\overline{r}+(\hat{i}-2\hat{j}+3\hat{k})|=2$
• C. $|\overline{r}-(\hat{i}-2\hat{j}+3\hat{k})|=\sqrt{10}$
• D. $|\overline{r}-(\hat{i}-2\hat{j}+3\hat{k})|=\sqrt{14}$

Answer 1

The correct option is A $|\overline{r}-(\hat{i}-2\hat{j}+3\hat{k})|=2$

Centre of the sphere is $(1,-2,3)$
Radius of sphere $=$ length of $\perp$ drawn from $1,-2,3$ to the plane
$\frac{|6\left(1\right)-3(-2)+2\left(3\right)-4|}{\sqrt{6^2+(-3{)}^2+2^2}}=2$
$\therefore$ required equation of sphere is
$|\overline{r}-(\hat{j}-2\hat{j}+3\hat{k})=$ radius of sphere $=2$