3. The binormal vector of a function r(t) is defined as B = T × N, where r' (t) ||r' (t)|| is the unit tangent vector and T(t): N(t) = = T'(t) ||T'(t)|| is the unit normal vector. Find the binormal vector for r(t) = (cost, sint, 0).
3. The binormal vector of a function r(t) is defined as B = T × N, where r' (t) ||r' (t)|| is the unit tangent vector and T(t): N(t) = = T'(t) ||T'(t)|| is the unit normal vector. Find the binormal vector for r(t) = (cost, sint, 0).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 3 Please
![2. Prove the following:
d [r • (r′ × r')] = r • (r′ × r”).
dt
3. The binormal vector of a function r(t) is defined as B = T × N, where
is the unit tangent vector and
T(t) =
N(t)
=
r'(t)
||r' (t)||
T' (t)
||T' (t)||
is the unit normal vector.
Find the binormal vector for r(t) = (cost, sint, 0).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F464fe16a-00d5-4182-8379-61bd4b8bbe02%2F15ddeead-ced7-4895-95e6-da0833d61fd9%2Fdiqbm4k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Prove the following:
d [r • (r′ × r')] = r • (r′ × r”).
dt
3. The binormal vector of a function r(t) is defined as B = T × N, where
is the unit tangent vector and
T(t) =
N(t)
=
r'(t)
||r' (t)||
T' (t)
||T' (t)||
is the unit normal vector.
Find the binormal vector for r(t) = (cost, sint, 0).
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