`A = 1/2 ⋅ |V| ⋅ |U| ⋅ sin(α) `
Enter a value for all fields
The Vector Area calculator Vectors U and V in three dimensions computes the area swept between two vectors (V and U) in Euclidean three dimensional space. This is the light blue area in the graphic.
INSTRUCTIONS: Enter the following in meters:
- (V): Vector V in meters
- (U): Vector U in meters
Area between Vectors (A): The calculator returns area in square meters. However, this can be automatically converted to compatible units via the pull-down menu.
The Math / Science
The Area between two Vectors (A) calculator computes the two dimensional area between two 3D vectors. The formula to compute the area is:
- Compute the length (magnitude) of both vectors. They represent the length of two legs of a triangle (|V| and |U|).
- Compute the angle between the vectors(α).
- Use the two lengths of and the angle to compute the area of the triangle, where:
A = 1/2 ⋅ |V| ⋅ |U| ⋅ sin(α)
This formula lets the user enter two three-dimensional vectors (V and U) with X, Y and Z components. Note the dot product of two unit vectors is equal to the cosine of the angle between the two vectors.
- k⋅V - scalar multiplication
- V/k - scalar division
- V / |V| - Computes the Unit Vector
- |V| - Computes the magnitude of a vector
- U + V - Vector addition
- U - V - Vector subtraction
- |U - V| - Distance between vector endpoints.
- |U + V| - Magnitude of vector sum.
- V • U - Computes the dot product of two vectors
- V x U - Computes the cross product of two vectors
- V x U • W - Computes the mixed product of three vectors
- Vector Angle - Computes the angle between two vectors
- Vector Area - Computes the area between two vectors
- Vector Projection - Compute the vector projection of V onto U.
- Vector Rotation - Compute the result vector after rotating around an axis.
- (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
- (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
- (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
- (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
- Vector Normal to a Plane Defined by Three Points