HELPPPPPO PLS RIGHT ANSWER PLSSSSSS axis, and $$ is the angle between the vector and the $z$ axis.

Learning Goal:

To use the dot product to find the components of

forces acting in arbitrary directions

A three$-$legged structure is shown below. It is

attached to the ground at points $B=(4\mathrm{.}44,0,0)$

and $C=(-4\mathrm{.}44,0,0)$ and connected to the

ceiling at point $A=(-5\mathrm{.}40,3\mathrm{.}19,5\mathrm{.}05).$ The

three legs connect at point $D=(0,2\mathrm{.}37,4\mathrm{.}00),$

where two forces, $F$ and $P,$ act. Force $F$ is given

by $F=4\mathrm{.}00i-13\mathrm{.}0j+27\mathrm{.}6kN$;$P$ has

magnitude $40\mathrm{.}0$ N and direction angles

$=119\mathrm{.}0,=34\mathrm{.}5,$ and $=73\mathrm{.}0$ for the $x$

$y,$ and $z$ axes, respectively. $($Figure $1)$

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

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Hint $1.$ Calculating components using the dot product

Hint $2.$ Calculate the $x$ component of a vector using the dot product

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Part B $-$ Finding the angle between forces

Part C $-$ Determining the force along a member

Determine the magnitude, $F_{DA},$ acting along member $DA,$ due to the applied force $F=4\mathrm{.}00i-13\mathrm{.}0j+27\mathrm{.}6kN.$

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

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Part D $-$ Finding the component of a force perpendicular to a direction

your answer in component form.

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

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