Calc 3 question (binormal, normal vectors)

[jaejoon89]

Hi, this is a calc 3 question. I know the binormal is given by

B = T x N

where
Binormal vector, B
Tangent vector, T
Normal vector, N

Also,
B = (R'(t) x R''(t)) / | R'(t) x R''(t) |
T = R'(t) / | R'(t) |

Does that mean
N = R''(t) / |R''(t)|?

 

[HallsofIvy]

Hi, this is a calc 3 question. I know the binormal is given by

B = T x N

where
Binormal vector, B
Tangent vector, T
Normal vector, N

Also,
B = (R'(t) x R''(t)) / | R'(t) x R''(t) |
T = R'(t) / | R'(t) |

Does that mean
N = R''(t) / |R''(t)|?

No.
[tex]\vec{N}= \frac{\vec{T}'}{|\vec{T}'|}[/itex]<br /> Which is NOT the same as <br /> R"/|R"|<br /> if |T| is not a constant.[/tex]