Find a normal vector to the surface $x ^ { 2 } + z ^ { 2 } = 5$ at the point $( 1,3 , - 2 )$ .
A) $\{ - 1,0,2 \}$

B) $\{ 1,3 , - 2 \}$
C) $\{ 1 , - 2,0 \}$
D) $\{ - 1,0 , - 3 \}$
E) $\{ 1,0 , - 2 \}$
F) $\{ 0,1 , - 2 \}$

G) $\{ 1,2,0 \}$

H)None of these

Question

Find a normal vector to the surface $x ^ { 2 } + z ^ { 2 } = 5$ at the point $( 1,3 , - 2 )$ .
A) $\{ - 1,0,2 \}$ 
 
B) $\{ 1,3 , - 2 \}$ 
C) $\{ 1 , - 2,0 \}$
D) $\{ - 1,0 , - 3 \}$ 
E) $\{ 1,0 , - 2 \}$
F) $\{ 0,1 , - 2 \}$ 
 
G) $\{ 1,2,0 \}$

H)None of these

Quizplus · Accepted Answer

The surface is given by the equation $x^2 + z^2 = 5$. The gradient vector $\nabla f = \{2x, 0, 2z\}$ is normal to the surface. At the point $(1, 3, -2)$, the normal vector is $\{2(1), 0, 2(-2)\} = \{2, 0, -4\}$, which simplifies to $\{1, 0, -2\}$.

Find a Normal Vector to the Surface x2+z2=5x ^ { 2 } + z ^ { 2 } = 5x2+z2=5

Find a Normal Vector to the Surface $x ^ { 2 } + z ^ { 2 } = 5$