Prove that `[hat(i)hat(j)hat(k)]=1, and [hat(i)hat(k)hat(j)]=-1`.

Explanation

To prove the given statements about the scalar triple product (also known as the box product), we will use the properties of the dot product and the cross product of unit vectors.

### Step-by-Step Solution:

1. **Understanding the Scalar Triple Product**:
The scalar triple product of three vectors \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) is defined as:
\[
[\mathbf{a} \mathbf{b} \mathbf{c}] = \mathbf{a} \cdot (\mathbf{b} \times \mathbf{c})
...