Answer
$r(t) =\lt 4 \cos t, 4 \sin t, 5-4 \cos t \gt$
Work Step by Step
Let us consider that $x=4 \cos t; y=4 \sin t$ for the first equation $x^2+y^2=16$
Now, consider the second equation $x+z=5$
This gives: $z=5 -x \implies z=5-4 \cos t$
Now, we will write the parametric equations in the vector form:
$r(t) =\lt 4 \cos t, 4 \sin t, 5-4 \cos t \gt$
