Learning Goal: Part C $-$ Position vector from $A$ to $C$

The length of cable $AC$ is $14\mathrm{.}2$ 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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Figure

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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$r_{BC}=,$ift,$jft,kft$

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 $z$ component with a magnitude

of $10$ lb $.$ What is the magnitude of the tension in the cable, $T_{BC}?$

Figure

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

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$T_{BC}=$

To find a position vector between two arbitrary points.

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

below $A$ by a distance $C_z=1\mathrm{.}90ft$ and

connected to $A$ by a cable $14\mathrm{.}2$ ft long. Cable $AC$

forms an angle $=19\mathrm{.}0$ with the positive $y$ axis. $B$

is $9\mathrm{.}50$ ft above $C$ and the distances $B_x$ and $B_y$

are $7\mathrm{.}70$ ft and $4\mathrm{.}50$ ft $,$ respectively. $($Figure $1)$

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

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 $AB$

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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$u_{AB}=,i,j,k$