Basic Vector Notations

There are several common ways to denote vectors in LaTeX:

1. Bold Vectors (using \\mathbf)

   \mathbf{v} = \mathbf{a} + \mathbf{b}

   Use \mathbf{v} for bold vector notation.

2. Arrow Vectors (using \vec)

   \vec{v} = \vec{a} + \vec{b}

   Use \vec{v} for vectors with arrows above.

3. Column Vectors

   \begin{pmatrix} x \\ y \\ z \end{pmatrix}

   Use matrix environments for column vector representation.

4. Row Vectors

   \begin{pmatrix} x & y & z \end{pmatrix}

Vector Operations

Common vector operations and their LaTeX representations:

1. Dot Product

   \mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^n a_i b_i

2. Cross Product

   \mathbf{a} \times \mathbf{b} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}

3. Vector Magnitude/Norm

   \|\mathbf{v}\| = \sqrt{v_1^2 + v_2^2 + v_3^2}

Advanced Vector Formatting

• Unit Vectors

  \hat{\imath}, \hat{\jmath}, \hat{k}

  Standard unit vectors using the hat notation.

• Vector Components

  \mathbf{v} = v_x\hat{\imath} + v_y\hat{\jmath} + v_z\hat{k}

• Vector Spaces

  \mathbf{v} \in \mathbb{R}^n

Best Practices

• Be consistent with your vector notation throughout your document
• Use \\mathbf for bold vectors in text and equations
• Use \\vec when you need to emphasize direction
• Use column vectors when working with matrices and transformations
• Consider using the physics package for advanced vector operations