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`|V| = sqrt(x^2 + y^2 + z^2)`

Enter a value for all fields

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

**INSTRUCTIONS:** Enter the following:

- (
**V**) : Enter the x, y and z components of V separated by commas (e.g. 2,9,3)

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

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:

`|V| = sqrt(x²+y²+z²)`

where:

- |V| 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.

**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

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