Learning Goal: Part C $-$ Determining the force along a member

Determine the magnitude, $F_{DA},$ acting along member $DA,$ due to the applied force $F=7\mathrm{.}00i-13\mathrm{.}0j+26\mathrm{.}2kN.$

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

View Available Hint$($s$)$

$F_{DA}=$

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 $B=(3\mathrm{.}35,0,0)$ and $C=(-3\mathrm{.}35,0,0)$

and connected to the ceiling at point $,$

$5\mathrm{.}74.$ The three legs connect at point $D=(0,3\mathrm{.}62,3\mathrm{.}00),$

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

$F=7\mathrm{.}00i-13\mathrm{.}0j+26\mathrm{.}2kN$;$P$ has magnitude $50\mathrm{.}0$ N

and direction angles $=130\mathrm{.}5,=75\mathrm{.}0,$ and

$=44\mathrm{.}4$ for the $x,y,$ and $z$ axes, respectively.$($Figure $1)$