Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate ∫ C ( x 2 + y 2 ) d s . C: counterclockwise around the circle x 2 + y 2 = 4 from (2, 0) to ( − 2 , 0 )
Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate ∫ C ( x 2 + y 2 ) d s . C: counterclockwise around the circle x 2 + y 2 = 4 from (2, 0) to ( − 2 , 0 )
Solution Summary: The author calculates a parametrization for the path C that is counterclockwise around the circle x2+y2.
Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b) evaluate
∫
C
(
x
2
+
y
2
)
d
s
.
C: counterclockwise around the circle
x
2
+
y
2
=
4
from (2, 0) to
(
−
2
,
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.
Find a plane containing the point (3, -3, 1) and the line of intersection of the planes 2x + 3y - 3z = 14
and -3x - y + z = −21.
The equation of the plane is:
Determine whether the lines
L₁ : F(t) = (−2, 3, −1)t + (0,2,-3) and
L2 : ƒ(s) = (2, −3, 1)s + (−10, 17, -8)
intersect. If they do, find the point of intersection.
● They intersect at the point
They are skew lines
They are parallel or equal
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