To find a position vector between two arbitrary points. As shown, two cables connect three points. C is below A by a distance Cz$=1\mathrm{.}50$ ft and connected to A by a cable $11\mathrm{.}0$ ft long. Cable AC forms an angle $\backslash$beta $=25\mathrm{.}0$ with the positive y axis. B is $9\mathrm{.}70$ ft above C and the distances Bx and By are $6\mathrm{.}50$ ft and $3\mathrm{.}10$ ft$,$ respectively. PART B: For the position vector found in Part A$,$ find the unit direction vector acting in the same direction. Express your answer in component form. PART C: The length of cable AC is $11\mathrm{.}0$ ft and the cable forms the angle $\backslash$beta $=25\mathrm{.}0$ with the y axis. Given this information and the dimensions provided in the figure, find the position vector from A to C$.$Express the position vector in component form. PART D: Find the position vector from B to C$.$Express your answer in component form. Express your answers, separated by commas, to three significant figures. PART E: A cable is attached between B and C$.$ The cable is attached in such a way that it has a tension of TBC along its length. The tensile force will attempt to pull B

toward C$.$ The force exerted on B has a z component with a magnitude of $10$ lb$.$ What is the magnitude of the tension in the cable, TBC$?$Learning Goal:

To find a position vector between two arbitrary points.

As shown, two cables connect three points. $C$ is

below $A$ by a distance $C_z=1\mathrm{.}50ft$ and

connected to $A$ by a cable $11\mathrm{.}0ft$ long. Cable $AC$

forms an angle $=25\mathrm{.}0$ with the positive $y$ axis. $B$

is $9\mathrm{.}70ft$ above $C$ and the distances $B_x$ and $B_y$

are $6\mathrm{.}50ft$ and $3\mathrm{.}10ft,$ respectively. $($Figure $1)$ Learning Goal:

To find a position vector between two arbitrary points.

As shown, two cables connect three points. $C$ is

below $A$ by a distance $C_z=1\mathrm{.}50ft$ and

connected to $A$ by a cable $11\mathrm{.}0ft$ long. Cable $AC$

forms an angle $=25\mathrm{.}0$ with the positive $y$ axis. $B$

is $9\mathrm{.}70ft$ above $C$ and the distances $B_x$ and $B_y$

are $6\mathrm{.}50ft$ and $3\mathrm{.}10ft,$ respectively. $($Figure $1)$