Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
Section 6-8 : Tangent, Normal and Binormal Vectors
For problems 1 – 3 find the unit tangent vector for the given vector function.
- \(\vec r\left( t \right) = {t^2}\,\vec i - \cos \left( {8t} \right)\vec j + \sin \left( {8t} \right)\vec k\)
- \(\vec r\left( t \right) = \left\langle {8t,2 - {t^6},{t^4}} \right\rangle \)
- \(\vec r\left( t \right) = \left\langle {\ln \left( {6t} \right),{{\bf{e}}^{1 - t}},5t} \right\rangle \)
For problems 4 & 5 find the tangent line to the vector function at the given point.
- \(\vec r\left( t \right) = \left\langle {3 + {t^2},{t^4},6} \right\rangle \) at \(t = - 1\).
- \(\vec r\left( t \right) = \left\langle {2t,{{\cos }^2}\left( t \right),{{\bf{e}}^{6t}}} \right\rangle \) at \(t = 0\).
For problems 6 & 7 find the unit normal and the binormal vectors for the given vector function.
- \(\vec r\left( t \right) = \left\langle {{{\bf{e}}^{4t}}\sin \left( t \right),{{\bf{e}}^{4t}}\cos \left( t \right),2} \right\rangle \)
- \(\vec r\left( t \right) = 2t\,\vec i + \frac{1}{2}{t^2}\,\vec j + \ln \left( {{t^2}} \right)\vec k\)