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 Scalar Product (Dot Product)

The scalar product (or dot product) of two vectors \(\vec{a}\) and \(\vec{b}\) is given by the formula:

\[
\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y + a_z b_z
...