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 . ) 184. x 2 − 8 x y z + y 2 + 6 z 2 = 0 , P ( 1 , 1 , 1 )
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 . ) 184. x 2 − 8 x y z + y 2 + 6 z 2 = 0 , P ( 1 , 1 , 1 )
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
.
)
184.
x
2
−
8
x
y
z
+
y
2
+
6
z
2
=
0
,
P
(
1
,
1
,
1
)
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.
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