Find the unit tangent vector \(\mathbf{T}(t)\).
\(\mathbf{r}(t) = (7 \cos t, 7 \sin t, 2)\), \(\mathbf{r}(\frac{\pi}{4}) = (\frac{7}{\sqrt{2}}, \frac{7}{\sqrt{2}}, 2)\)
\(\mathbf{T}(\frac{\pi}{4}) = (-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0)\)
Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization.)
\((\frac{7}{\sqrt{2}} - \frac{1}{\sqrt{2}}t, \frac{7}{\sqrt{2}} + \frac{1}{\sqrt{2}}t, 4)\)