$1.)$ For the mechanism below:

a$)$ Draw the vector diagram with all the necessary parameters required to define the mechanism. Draw the vector diagram next to the mechanism diagram. $[5]$

b$)$ Specify which parameters in the vector diagram are a function of time. $($Block B slides along the bent object.$)[3]$

c$)$ Write the position equation in the complex number format. Incorporate the length of the constant values and simplify the equation. $[5]$

d$)$ Derive the velocity equation from the position equation. Expand and simplify the derivative in all terms. $[5]$

e$)$ Break down the complex velocity equation in terms of the real and imaginary component equations. $[2]$

Block B slides along the bent object. The bent object forms a right angle at point A $.$