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.

Vectors

Find plots and various other properties of vectors.

Compute properties of a vector:

vector {2, -5, 4}

Specify a vector as a linear combination of unit vectors:

vector 3i + 5j

vector 2i - 4j + 3k

Compute the norm of a vector:

norm {12, -5}

More examples

Vector Algebra

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

Do vector computations:

vector (1,3,-1) + (-2,1,6)

7 {1, 0, -2, 1} - 4 {2, -1, 1, -1}

(i + j + k) + (2i - 3j + 8k)

Compute a dot product:

{12, 20} . {16, -5}

(7i-j+3k).(4i-2k)

Compute a cross product:

{1/4, -1/2, 1} cross {1/3, 1, -2/3}

(8i + 3j - k) x (i - j + 2k)

Compute a (scalar) cross product in two dimensions:

(4,1) x (-5,6)

Normalize a vector:

normalize the vector (3, 10)

normalize vector

Convert to another coordinate system:

(1,1,-3) in spherical coordinates

More examples