Suppose that a ground robot is moving forward in the positive x$-$direction and its heading vector

is v $=(1,0,0).$ The robot executes a $120-$degree left turn $($counter$-$clockwise$)$ about the z$-$axis.

$($a$)[0\mathrm{.}5$ pts$]$ Represent the robot$$s heading as a quaternion.

$($b$)[0\mathrm{.}5$ pts$]$ Represent the turn as a quaternion.

$($c$)[1$ pts$]$ Calculate the robot$$s new heading vector after the turn $($by using quaternion mul$-$

tiplications$)$