For the following exercises, find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P 0 ( x 0 , y 0 , z 0 ) and a vector n = ( a. b. c ) that is parallel to the line. Then the equation of the line is x − x 0 = a t , y − y 0 = b t , z − z 0 = c t . ) 185. z = ln ( 3 x 2 + 7 y 2 + 1 ) , P ( 0 , 0 , 0 )
For the following exercises, find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, P 0 ( x 0 , y 0 , z 0 ) and a vector n = ( a. b. c ) that is parallel to the line. Then the equation of the line is x − x 0 = a t , y − y 0 = b t , z − z 0 = c t . ) 185. z = ln ( 3 x 2 + 7 y 2 + 1 ) , P ( 0 , 0 , 0 )
For the following exercises, find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line,
P
0
(
x
0
,
y
0
,
z
0
)
and a vector
n = ( a. b. c ) that is parallel to the line. Then the
equation of the line is
x
−
x
0
=
a
t
,
y
−
y
0
=
b
t
,
z
−
z
0
=
c
t
.
)
185.
z
=
ln
(
3
x
2
+
7
y
2
+
1
)
,
P
(
0
,
0
,
0
)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.