Find the scalar and vector paroducts of two vectors. `a=(3hat(i)-4hat(j)+5hat(k)) " and " b=(-2hat (i) +hat(j)-3hat(k))`

Explanation

To find the scalar and vector products of the vectors \( \mathbf{a} = 3\hat{i} - 4\hat{j} + 5\hat{k} \) and \( \mathbf{b} = -2\hat{i} + \hat{j} - 3\hat{k} \), we will follow these steps:

### Step 1: Calculate the Scalar Product (Dot Product)

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

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