Name:

Part $1(3$ points each, $15$ points total$)$

Which of the following can be used to find the angle between two vectors?

A$.$ Vector addition

B$.$ Cross product

C$.$ Dot product

D$.$ Vector transmission

E$.$ Vector triple product

Which gives $A*B,$ where $A=A_{x}i+A_{y}j+A_{z}k$ and $B=B_{x}i+B_{y}j+B_{z}k?$

A$.(A_x+B_x)i+(A_y+B_y)j+(A_z+B_z)k$

B$.A_x{B}_x+A_y{B}_y+A_z{B}_z$

C$.A_x{B}_{x}i+A_y{B}_{y}j+A_z{B}_{z}k$

D$.(A_x+B_x)+(A_y+B_y)+(A_z+B_z)$

$AC$ is $6$ m long and has its center of gravity at $B.DE$ is a $6$ m pole

rigidly fixed to the ground at $D.$ Sketch the best location of a cable

connecting $C$ to pole $DE$ if the goal is to minimize the force in the

cable $($neglect the horizontal distance from $D$ to $A).$

Briefly $($no more than $10$ words$)$ explain your answer.

Instead of using a pole and cable, you can use a mechanism to apply a

couple to support $AC.$ Show how you would place it if the goal is to

minimize the couple.

Briefly $($no more than $10$ words$)$ explain your answer.