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 $14\mathrm{.}3$ ft long. Cable $AC$ forms an angle $=19\mathrm{.}0$ with the positive $y$ axis. $B$ is $8\mathrm{.}70$ ft above $C$ and the distances $B_z$ and $B_y$ are $8\mathrm{.}70$ ft and $4\mathrm{.}50$ ft respectively. $($Figure $1)$

Using the dimensions in the figure, find the position v

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 $14\mathrm{.}3$ ft long. Cable $AC$ forms an angle $=19\mathrm{.}0$ with the positive $y$ axis. $B$ is $8\mathrm{.}70$ ft above $C$ and the distances $B_z$ and $B_y$ are $8\mathrm{.}70$ ft and $4\mathrm{.}50$ ft respectively. $($Figure $1)$

Using the dimensions in the figure, find the position vector from $A$ to $B$ in component form.

Express your answers, separated by commas, to three significant figures.

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Part B $-$ Unit direction vector for line $AB$

Forector from $A$ to $B$ in component form.

Part A

xpress your answers, separated by commas, to three significant figures.

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Part B $-$ Unit direction vector for line $AB$

For the position vector found in Part A$,$ find the unit direction vector acting in the same direction. Express your answer in component form. Express your answers, separated by commas, to three significant figures.

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Part C $-$ Position vector from $A$ to $C$

The length of cable $AC$ is $14\mathrm{.}3$ ft $,$ and the cable forms the angle $=19\mathrm{.}0$ 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

Express your answers, separated by commas, to three significant figures.

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Part D $-$ Position vector from $B$ to $C$

Find the position vector from $B$ to $C.$ Express your answer in component form. Express your answers, separated by commas, to three significant figures.

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Part E $-$ Tension in the cable

A cable is attached between $B$ and $C.$ The cable is attached in such a way that it has a tension of $T_{BC}$ along its length. The tensile force will attempt to pull $B$ toward $C.$ The force exerted on $B$ has a component with a magnitude of $10$ lb $.$ What is the magnitude of the tension in the cable, $T_{BC}?$

Express your answer to three significant figures and include the appropriate units.

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As shown, two cables connect three points. $C$ is below $A$ by a distance $C_z=1\mathrm{.}50ft$ and connected to $A$ by

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 $14\mathrm{.}3$ ft long. Cable $AC$ forms an angle $=19\mathrm{.}0$ with the positive $y$ axis. $B$ is $8\mathrm{.}70$ ft above $C$ and the distances $B_x$ and $B_y$ are $8\mathrm{.}70$ ft and $4\mathrm{.}50$ ft respectively $($Figure $1)$

Figure

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Part B $-$ Unit direction vector for line $AB$

Part C $-$ Positio