Let S be the sphere of radius 4 centered at the origin, oriented outward. Find $\vec { n }$ , the unit normal vector to S in the direction of orientation.
A) $\vec { n } = \frac { x } { 4 } \vec { i } + \frac { y } { 4 } \vec { j } + \frac { z } { 4 } \vec { k }$
B) $\vec { n } = x \vec { i } + y \vec { j } + z \vec { k }$
C) $\vec { n } = \frac { x ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { i } + \frac { y ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { j } + \frac { z ^ { 2 } } { \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } } \vec { k }$
D) $\vec { n } = \frac { x } { 16 } \vec { i } + \frac { y } { 16 } \vec { j } + \frac { z } { 16 } \vec { k }$

Question

Quizplus · Accepted Answer

The unit normal vector $\vec{n}$ for a sphere centered at the origin with radius $r$ is given by $\vec{n} = \frac{1}{r}(x\vec{i} + y\vec{j} + z\vec{k})$. Since the radius is 4, $\vec{n} = \frac{x}{4}\vec{i} + \frac{y}{4}\vec{j} + \frac{z}{4}\vec{k}$.

Let S Be the Sphere of Radius 4 Centered at the Origin