Problem $3[30$ points$]$

Summary: $3$D Compilation

This is an exam question and should not be distributed. Any question bank that hosts or provides solutions to this question will be participating in an act of academic dishonesty$]$

Figure $3$ shows a $3$ in by $6$ in by $9$ in block acted on by two forces as shown $($one across the front face, one at the back corner, parallel to the $x-$axis$).$ For the given force system and geometry:

$($a$)$ Find the unit vector hat$(u{)}_{AB}$ that describes the direction from point $A$ to point $B$

$[8$ points$]$

$($b$)$ What is the vector sum of vec$(F{)}_1+$vec$(F{)}_2?$ Express your answer in Cartesian form

$[6$ points$]$

$($c$)$ What is the magnitude of the vector you just solved for in part $b?($note: you do not have to find the direction$)$

$[6$ points$]$

$($d$)$ How would you solve for the moment of vec$(F{)}_2$ about point $O.$ Your answer should be a cross product $($also known as a determinant$)$ that includes a correct position vector and force vector $($note: you do not have to solve the cross product, just set it up$)[10$ points$]$