Examples for


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 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:

Vector Projections

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

Compute the projection of one vector onto another:

Project a vector onto an axis:

Project a vector onto a plane:

Explore vector projections in higher dimensions:

Vector Algebra

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: