Chapter 14 - Calculus of Vector-Valued Functions - 14.1 Vector-Valued Functions - Exercises - Page 709: 6

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

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