Learning Goal:

To find a force's directional components that act along a cable and to find the coordinates

of a point on a cable that has a force vector applied to it

Three$-$dimensional Cartesian force vectors are used throughout engineering mechanics.

The generic force vector is represented as follows:

$F=F_{x}i+F_{y}j+F_{z}k$

where $F$ is the force vector and $F_z,F_y,$ and $F_z$ are the vector' $i,j,$ and $k$ components,

respectively. The force vector has a magnitude $F=\sqrt[\phantom{2}]{F_x^2+F_y^2+F_x^2}.$ The vector's

direction is described by a unit vector $u,$ where $u=\frac{F}{F}.$

PartA

As shown, a force vector $F$ vith a magnitude of $c=115N$ is applied at point A and is directed toward point $C.($Eigure $1)$ The distance $a$ is $1\mathrm{.}40$ m and the distance $b$ is $0\mathrm{.}800$ m $.$ What are the $i,j,$ and $k$ components

of $F?$

Express your answers numerically in newtons to three significant figures separated by commas.

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Part B

As shown, the cable OA exerts a force on point O of $F=F_{x}i+F_{j}j+F_{z}k($Figure $2)$ If the cable's length is $a,$ what are the $x,y,$ and $z$ coordinates of $A$ in terms of $a,F_x,F_y,$ and $F_z?$

Express your answers in terms of $a,F_x,F_y,$ and $F_z$ separated by commas.

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