Properties of space curves Do the following calculations. a. Find the tangent vector and the unit tangent vector. b. Find the curvature. c. Find the principal unit normal vector. d. Verify that | N | = 1 and T · N = 0. e. Graph the curve and sketch T and N at two points. 61. r ( t ) = cos t i + 2 cos t j + 5 sin t k , for 0 ≤ t ≤ 2 π
Properties of space curves Do the following calculations. a. Find the tangent vector and the unit tangent vector. b. Find the curvature. c. Find the principal unit normal vector. d. Verify that | N | = 1 and T · N = 0. e. Graph the curve and sketch T and N at two points. 61. r ( t ) = cos t i + 2 cos t j + 5 sin t k , for 0 ≤ t ≤ 2 π
Properties of space curvesDo the following calculations.
a.Find the tangent vector and the unit tangent vector.
b.Find the curvature.
c.Find the principal unit normal vector.
d.Verify that |N| = 1 and T · N = 0.
e.Graph the curve and sketchTandNat two points.
61.
r
(
t
)
=
cos
t
i
+
2
cos
t
j
+
5
sin
t
k
,
for
0
≤
t
≤
2
π
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.
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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