Answer
$r(t) =\lt 4 \cos t, 4 \sin t, 5-4 \cos t \gt$
Work Step by Step
Need to write $x=4 \cos t \\ y=4 \sin t$ for the first equation $x^2+y^2=16$
We have the second equation as: $x+z=5$
After solving, we get
$z=5 -x$ and $z=5-4 \cos t$
Write the parametric equations in the vector form, then we get
$r(t) =\lt 4 \cos t, 4 \sin t, 5-4 \cos t \gt$
