1. The problem asks to analyze the expression $a \cdot (b \times a)$ and determine its nature. 2. Recall that $b \times a$ is the cross product of vectors $b$ and $a$, which results in a vector perpendicular to both $b$ and $a$. 3. The dot product $a \cdot (b \times a)$ is the scalar triple product, which can be interpreted as the volume of the parallelepiped formed by vectors $a$, $b$, and $a$. 4. Since the vector $a$ appears twice in the scalar triple product, the volume is zero because the parallelepiped collapses (two vectors are the same). 5. Therefore, $a \cdot (b \times a) = 0$. 6. This means the expression is equal to zero, so the correct answer is (c) is equal to 0.