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How can I mark my question as SOLVED?

Dhamnekar Winod

Active member
Nov 17, 2018
101
Continuing this exercise, assume that f'(t) and f''(t) are not parallel. Then $T'(t)\not=0$ so we can define unit principal normal vector N by
$$N(t)=\frac{T'(t)}{||T'(t)||}$$

Now how to show that $$N(t)=\frac{f'(t)\times (f''(t)\times f'(t))}{||f'(t)||*(||f''(t)\times f'(t)||)}$$

Continuing this execise we can define unit binormal vector B $$B(t)=T(t)\times N(t)$$ where $$T(t)=\frac{f'(t)}{||f'(t)||}$$. Note: We have already defined T'(t).
Now how to show that $$B(t)=\frac{f'(t)\times f''(t)}{||f'(t)\times f''(t)||}$$
I want to continue this exercise with one more question related to this question. How does the vectors T(t), N(t), B(t)form a right-handed system of mutually perpendicular unit vectors (called orthonormal vectors) at each point on the curve f(t)? In the answer to this question, I want to clear explanation about Osculating plane, Normal plane and Rectifying plane.:)
Hello,
How can i mark this question (thread) " SOLVED"
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,736
I've adjusted your permissions so that you can edit indefinitely. So now, you can go to the thread and click the "More options" button (to the right of the "Watch" button) to edit the thread and add the [SOLVED] prefix. :)