$($Kinematics $$ Numerical programming $30$ pt$)$ Frame B is rotating relative to Frame

I with a constant rate, $\backslash$omega $.$ At time t $=0$ sec$,$ Frame B defines the identical directions

to Frame I. Assume that

$\backslash$omega

B $=$

$$

$$

$1$

$1$

$1$

$$

$(1)$

Frame B evolves from the original condition with time. Let$$s consider a constant

position vector in B$,$rB$,$ which is given as

$$rB $=$

$$

$$

$2$

$1$

$0$

$$

$(2)$

Calculating a proper rotational matrix, rewrite this vector in I, $$rI

$,$ at t $=35$ sec

numerically. Hint: Ensure the derived rotational matrix meets three key features $($see

Lecture $2).$ Also, you may use programming$-$embedded integrators such as ode$45$ in

Matlab.