Find the unit normal and binormal vectors for the circular helix mathb | Mathematics I 2081

Mathematics I20815 marksNumerical: normal and binormal vectorsNormal and binormal vectors

Find the unit normal and binormal vectors for the circular helix $\mathbf{r}(t) = \cos t \hat{i} + \sin t \hat{j} + t \hat{k}$ . [5]

Find the unit normal and binormal vectors for the circular helix $\mathbf{r}(t) = \cos t \hat{i} + \sin t \hat{j} + t \hat{k}$. [5]

$\mathbf{r}(t) = \cos t\,\hat{i} + \sin t\,\hat{j} + t\,\hat{k}$ All data present and readable. --- $\mathbf{r}'(t) = -\sin t\,\hat{i} + \cos t\,\hat{j} + \hat{k}$ $\mathbf{r}'(t) = \sqrt{\sin^2 t + \cos^2 t + 1} = \sqrt{2}$ $$\mathbf{T}(t) = \frac{1}{\sqrt{2}}\left(-\sin t,\hat{i} + \cos ...

$$\mathbf{r}(t) = \cos t,\hat{i} + \sin t,\hat{j} + t,\hat{k}$$ All data present and readable. --- $$\mathbf{r}'(t) = -\sin t,\hat{i} + \cos t,\hat{j} + \hat{k}$$ $$\mathbf{r}'(t) = \sqrt{\sin^2 t + \cos^2 t + 1} = \sqrt{2}$$ $$\mathbf{T}(t) = \frac{1}{\sqrt{2}}\left(-\sin t,\hat{i} + \cos ...

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Find the unit normal and binormal vectors for the circular helix mathbfr(t) = cos t hati + sin t hatj + t hatk.