#### Answer

$$\langle -1,5,\frac{1}{2} \rangle .$$

#### Work Step by Step

Since we have
$$ r(t)=(4-t)i+(2+5t)j+\frac{1}{2}tk $$
then we rewrite $ r(t)$ as follows
$$ r(t)=(4,2,0)+t\langle -1,5,\frac{1}{2} \rangle .$$
Hence, the direction vector is given by
$$\langle -1,5,\frac{1}{2} \rangle .$$