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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
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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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).
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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