Suppose you want to compute the scalar (dot) product of two vectors:

\[ \mathbf{u} = \begin{pmatrix} 2 \\ -3 \\ 1 \end{pmatrix}, \quad \mathbf{v} = \begin{pmatrix} 4 \\ 0 \\ -2 \end{pmatrix} \]

1. Create a new document and select Add Calculator.
2. Enter the two vectors:
   • Press and select Matrix & Vector > Create > Vector.
   • Enter the dimensions (3) for both vectors and input their components: \( \mathbf{u} = [2, -3, 1] \) and \( \mathbf{v} = [4, 0, -2] \).
3. Compute the scalar product:
   • Press and select Matrix & Vector > Vector Operations > Dot Product.
   • Enter u, v and press .

The result should be \( 8 + 0 - 2 = 6 \). Thus, \( \mathbf{u} \cdot \mathbf{v} = 6 \).

Suppose you want to compute the vector (cross) product of the following vectors:

\[ \mathbf{u} = \begin{pmatrix} 2 \\ -3 \\ 1 \end{pmatrix}, \quad \mathbf{v} = \begin{pmatrix} 4 \\ 0 \\ -2 \end{pmatrix} \]

1. Create a new document and select Add Calculator.
2. Enter the two vectors:
   • Press and select Matrix & Vector > Create > Vector.
   • Enter the dimensions (3) for both vectors and input their components: \( \mathbf{u} = [2, -3, 1] \) and \( \mathbf{v} = [4, 0, -2] \).
3. Compute the vector product:
   • Press and select Matrix & Vector > Vector Operations > Cross Product.
   • Enter u, v and press .

The result should be: \[ \mathbf{u} \times \mathbf{v} = \begin{pmatrix} 6 \\ -10 \\ 12 \end{pmatrix} \]