Question $2$

$[15]$

a$.$ The end effector of a robot is translated in the x $-,$ y $-$ and z $-$ directions by distance of $5\mathrm{.}5,10\mathrm{.}5$ and $15\mathrm{.}5$ respectively. Write the transformation matrix. If the initial position of the end$-$effector is $(4,1,5,$ what is the final position of the end$-$effector?

b$.$ A point $($end$-$effector position$)$ is rotated about the $z-$axis by an angle of $35.$ Write the transformation matrix. The initial position of the end$-$effector before rotation us $(4,3,1).$ Determine the new position of this point.