Find the scalar and vector products of two vectors `vec(a)=(2hat(i)-3hat(j)+4hat(k))` and `vec(b)= (hat(i)-2hat(j)+3hat(k))`.

Explanation

To find the scalar and vector products of the vectors \(\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}\) and \(\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}\), we will follow these steps:

### Step 1: Calculate the Vector Product (\(\vec{a} \times \vec{b}\))

The vector product (cross product) can be calculated using the determinant of a 3x3 matrix formed by the unit vectors and the components of the vectors \(\vec{a}\) and \(\vec{b}\).

\[
\vec{a} \times \vec{b} = \begin{vmatrix}
...