V3 - Vector Magnitude

The Vector Magnitude calculator computes the magnitude |V| of a three dimensional vector (V).

INSTRUCTIONS:  Enter the following:

• (`vecV`) :  Vector V 

Vector Magnitude |V|: The calculator returns the magnitude of the vector (e.g.9.69)

The Math / Science

This formula lets the user enter a three dimensional vector with X, Y and Z components and calculates the magnitude of the vector |V|.   The formula to compute the vector magnitude is:

           `|vecV| = sqrt(x²+y²+z²)`

where:

• |`vecV`| is the magnitude of the vector
• x, y and z are the components of the vector.

Visually, the magnitude of the vector is the length of measurement from the origin of the coordinate system to the end point of the vector.

3D Vector Functions

• 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.
• Vector Components 3D - Returns a vector's magnitude, unit vector, spherical coordinates, cylindrical coordinates and angle from each 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
• (x,y) to (r, θ) - Cartesian to Polar
• (r, θ) to (x,y) - Polar to Cartesian 
• Vector Normal to a Plane Defined by Three Points

Box Calculators

• Rolling Offset (run) - Equation to calculate the run (R) in the diagram above.
• Magnitude of a 3D Vector
• surface area of a box,
• volume of a box,
• diagonal of a box and
• weight of a box if full when you provide the mean density
• weight of a box if full and you can select any of 500+ substances

References

• Light and Matter by Benjamin Crowell, Chapter 7.1 Vector Notation
• University Physics 12th Edition, Chapter 1, Equation #1.12