Get help with parametric equations

Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.)
Point: (-3, 4, 5)
Parallel to: \(\displaystyle\frac{{{x}-{1}}}{{2}}=\frac{{{y}+{1}}}{ -{{3}}}={z}-{5}\)
(a) Parametric equations
(b) Symmetric equations

A vector-valued function \(r(t)\) with its defining parametric equations is given by the following.
\(x = f(t)\)
\(y = g(t)\)
\(r(t) = ft(i) + g(t)j\)
Now find the vector-valued function \(r(t)\) with the given parametric equations.

Polar coordinates of point P are given. Find all of its polar coordinates.
\(\displaystyle{P}={\left({1},-\frac{\pi}{{4}}\right)}\)

Surface s is a part of the paraboloid \(\displaystyle{z}={4}-{x}^{{2}}-{y}^{{2}}\) that lies above the plane \(z=0\).\((6+7+7=20pt)\)

a) Find the parametric equation \(\displaystyle\vec{{r}}{\left({u},{v}\right)}\) of the surface with polar coordinates \(\displaystyle{x}={u}{\cos{{\left({v}\right)}}},{y}={u}{\sin{{\left({v}\right)}}}\) and find the domain D for u and v.

b) Find \(\displaystyle\vec{{r}}_{{u}},\vec{{r}}_{{v}},\) and \(\displaystyle\vec{{r}}_{{u}}\cdot\vec{{r}}_{{v}}\).

c) Find the area of the surface

\(x = t− \sin t\)
\(y = 1 − \cos t −\) curve given by the parametric equation \(\displaystyle=\frac{\pi}{{3}}\) in point
Find the equation of the tangent line

Use the given graph of f over the interval (0,7) to find the following.

Determine the line integral along the curve C from A to B. Find the parametric form of the curve C
Use the vector field:
\(\overrightarrow{F}=[-bx\ cy]\)
Use the following values: \(a=5,\ b=2,\ c=3\)