Cable Displacement Vectors

In structural construction, cable lines are installed to anchor tall towers. Construction managers must determine the length and spatial direction of the cables from the coordinates of the anchor points to ensure proper procurement and site layout.

A support tower has its base at the origin and rises vertically along the $z$-axis. A cable is to be connected from a point $P(0, 0, 45)\text{ meters}$ high on the tower to a ground anchor situated at $Q(15, -20, 0)\text{ meters}$.

1. Find the displacement vector $\vec{PQ}$ representing the cable in component form.
2. Find the total length of the cable required (the magnitude of the vector).
3. Find the unit vector in the direction of the cable.