$$

$$ Learning Goal:

As shown, three forces act on the tip of a pole.

$F_1=-60i+145j+45k$ lb$.F_2=130lb$ and forms

the following angles with the $x,y,$ and $z$ axes, respectively:

$=51\mathrm{.}7,=66\mathrm{.}1,$ and $=132\mathrm{.}2.F_3=100lb,$

forms the angle $=30$ with the $z$ axis, and forms the angle

$=25$ between the $x$ axis and the proiection of $F_3$ in the $xy$

Find the resultant of adding $F_1,F_2,$ and $F_3.$ Express your answer in component form.

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

View Available Hint$($s$)$

$R_{123}=$

ilb,$jlb,klb$

Part C $-$ Direction of a resultant

For the given forces, $F_1,F_2,$ and $F_3,$ find the three direction angles ${}_R,{}_R,$ and ${}_R$ between the resultant force $R_{123}$ found in Par

and $z$ axes, respectively.

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

View Available Hint$($s$)$

${}_R,{}_R,{}_R=$

$,,$ As shown, three forces act on the tip of a pole.

$F_1=-60i+145j+45klb.F_2=130lb$ and forms

the following angles with the $x,y,$ and $z$ axes, respectively:

$=51\mathrm{.}7,=66\mathrm{.}1,$ and $=132\mathrm{.}2.F_3=100lb,$

forms the angle $=30$ with the $z$ axis, and forms the angle

$=25$ between the $x$ axis and the projection of $F_3$ in the $xy$

As shown, a force of $300$ lb acts at the tip of a tower. Two of the force's direction angles are known, ${}_{R1}=35\mathrm{.}5$ and ${}_{R1}=68\mathrm{.}5,$ that define the

angles between the force and the $y$ and $z$ axes, respectively. Find ${}_{R1},$ the angle between the $x$ axis and the force.

Express your answer in degrees to three significant figures.

p

View Available Hint$($s$)$

${}_{R1}=$