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, 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:

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:

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: