The angle between $$A$$ and $$B$$ is $$\theta .$$ The value of the triple product $$A \cdot \left( {B \times A} \right)$$   is

Solution :
In scalar triple product of vectors, the positions of dot and cross can be interchanged, i.e.
$$\eqalign{ & A \cdot \left( {B \times A} \right) = \left( {A \times B} \right) \cdot A = \left( {A \times A} \right) \cdot B \cr & {\text{but}}\,A \times A = 0 \cr & \therefore A \cdot \left( {B \times A} \right) = 0 \cr} $$
Alternative
$$\eqalign{ & A \cdot \left( {B \times A} \right) \cr & {\text{Let}}\,\,A \times B = C \cr} $$
The direction of $$C$$ is $$ \bot $$ to $$A$$ and $$B$$ from cross product formula
So, $$A \cdot C = 0$$     (since, $$A$$ and $$C$$ are $$ \bot $$ to each other)