Question

The equation $|\overline{r}{|}^2-2(\overline{r}.\overline{a})+\lambda =0$ represent a

• A. Straight line
• B. Plane
• C. Sphere
• D. None of these

Answer 1

The correct option is C Sphere

Let $\overline{r}=x\hat{i}+y\hat{j}+z\hat{k}$
$|\overline{r}{|}^2-2(\overline{r}\cdot \overline{a})+\lambda =0$
$\therefore x^2+y^2+z^2-2(\overline{r}\cdot \overline{a})+\lambda =k\left(k\lambda R\right)$
$\therefore x^2+y^2+z^2=k-\lambda +2\overline{a}\cdot \overline{a}$
$x^2+y^2+z^2=+ve$ real number which is a sphere