Q. The vector equation of the sphere whose centre is the point (1,0,1)and radius is 4, is
A) $|\overrightarrow{\mathbf{r}} - \left( \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}} \right)| = 4$
B) $|\overrightarrow{\mathbf{r}} + \left( \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}} \right)| = 4^{2}$
C) $|\overrightarrow{\mathbf{r}} \bullet \left( \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}} \right)| = 4$
D) $|\overrightarrow{\mathbf{r}} \bullet \left( \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}} \right)| = 4^{2}$
Explanation
(a)
Given centre of sphere=(1, 0, 1) and radius=4
$\therefore$Vector equation of sphere is
$\ \left| \overrightarrow{\mathbf{r}} - \overrightarrow{\mathbf{a}} \right| = R\$Where $\overrightarrow{\mathbf{a}}\$centre of sphere and $R\$radius of sphere.
Hence, the vector equation of sphere is
$\left| \overrightarrow{\mathbf{r}} - \left( \widehat{\dot{\mathbf{i}}} + \widehat{\mathbf{k}} \right) \right| = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.