This exam is closed book and closed notes. Problem $1$ is worth $30$ points, problem $2$ is worth $25$ points

and problem $3$ is worth $30$ points. The weighting reflects both level of difficulty and amount of work

involved to solve the problem, so please allocate your time wisely. All work must be shown in order to

get full credit, especially free body diagrams!

Problem $1(30$ points$)$:

In the following structure,

$($a$)$ Determine the angle $$ between the cables

$AB$ and $AC.$

$($b$)$ Determine the component of the force

vec$(F)=(100$hat$()-600$hat$()+300$widehat$(k))N$ acting along

the direction $BA(F_{BA}).$

$($c$)$ Find the unit normal $($ widehat$(u{)}_N)$ of the triangle

formed by points $A,B$ and C which has a

positive $z-$component.

$($d$)$ Decompose vec$(F)$ into vector components

parallel $(vec(F{)}_{||})$and perpendicular to

this normal direction.