Examples for

# Vectors

Vectors are objects in an n-dimensional vector space that consist of a simple list of numerical or symbolic values. Wolfram|Alpha can convert vectors to spherical or polar coordinate systems and can compute properties of vectors, such as the vector length or normalization. Additionally, Wolfram|Alpha can explore relationships between vectors by adding, multiplying, testing orthogonality and computing the projection of one vector onto another.

Find plots and various other properties of vectors.

#### Compute properties of a vector:

#### Specify a vector as a linear combination of unit vectors:

#### Compute the norm of a vector:

Explore the orthogonality relationship on sets of vectors.

#### Check if the set of vectors is orthogonal:

#### Find conditions for orthogonality between vectors with symbolic components:

Perform arithmetic and algebraic operations, such as dot and cross product, on vectors.

#### Do vector computations:

#### Compute a dot product:

#### Compute a cross product:

#### Compute a (scalar) cross product in two dimensions:

#### Normalize a vector:

#### Convert to another coordinate system:

Compute and visualize the projection of a vector onto a vector, axis, plane or space.