The magnitude of the zero vector is zero.
The zero vector is a vector with all components equal to zero. It is represented by a single boldface zero: 0. Since it has no length or direction, its magnitude is zero.
Here are some examples of zero vectors in different dimensions:
- In 2D: (0, 0)
- In 3D: (0, 0, 0)
- In n-dimensional space: (0, 0, ..., 0)
The magnitude of a vector is its length, which is calculated using the Pythagorean theorem. For a vector v = (v<sub>1</sub>, v<sub>2</sub>, ..., v<sub>n</sub>), the magnitude is:
||v|| = √(v<sub>1</sub><sup>2</sup> + v<sub>2</sub><sup>2</sup> + ... + v<sub>n</sub><sup>2</sup>)
When all components are zero, the magnitude becomes:
||0|| = √(0<sup>2</sup> + 0<sup>2</sup> + ... + 0<sup>2</sup>) = √0 = 0
Therefore, the magnitude of the zero vector is always zero, regardless of the dimension.
