Given unit vectors $\boldsymbol { a } , \boldsymbol { b }$ with an angle of $45 ^ { \circ }$ between them, and $k \boldsymbol { a } - \boldsymbol { b}$ is perpendicular to $\boldsymbol { a }$ , then $k = $ $\_\_\_\_$.
$\frac{\sqrt{2}}{2}$
Given unit vectors $\boldsymbol { a } , \boldsymbol { b }$ with an angle of $45 ^ { \circ }$ between them, and $k \boldsymbol { a } - \boldsymbol { b}$ is perpendicular to $\boldsymbol { a }$ , then $k = $ $\_\_\_\_$.