Chapter 2: Space Curves

Section 2.6: Binormal and Torsion

Example 2.6.5

$$ Show that the definition $\mathbf{B}\=\mathbf{T}\times \mathbf{N}$ implies $∥\mathbf{B}∥\=1$. $$ Solution $$ The orthogonal vectors T and N are both unit vectors.   By the definition of B, if $\mathrm{\θ}\=\mathrm{\π}\/2$ is the angle between T and N,   $∥\mathbf{B}∥$ = $∥\mathbf{T}\times \mathbf{N}∥$ = $∥\mathbf{T}∥ ∥\mathbf{N}∥$ $\sin \left(\mathrm{\θ}\right)$ = $1\cdot 1\cdot \sin \left(\mathrm{\π}\/2\right)$ = $1$ $$

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