A metal bracket positioned at the origin $P_0=[0,0,0]$ of the model coorainate system

has bolt holes positioned at $P_1=[-1,2,0{]}^{TT}$ and $P_2=[2,0,2{]}^{TT}.$ If the metal bracket is

rotated by $45$ about the $Y-$axis, translated by $t=-1$hat$()+3$hat$()+2$hat$(k),$ then reflected over the

X$-$Z plane:

a$)$ State which matrices should be multiplied to give the homogeneous

transformation matrix. $(5$ marks$)$

b$)$ Find the new bolt hole locations. $(10$ marks$)$

c$)$ Describe, through sketches and words, why using geometric dimensioning and

tolerancing techniques could be advantageous when specifying the bolt hole

location. $(5$ marks$)$