# Is (0,0,0) an undefined vector?

I'm not sure what to make of the direction of a vector with components (0,0,0). Is it an undefined vector?

-

– Qmechanic♦ Nov 11 '11 at 22:01

## 2 Answers

There's absolutely nothing wrong with a vector having all zero components. But a vector like that does have an undefined direction. So the definition of a vector as "something which has a magnitude and a direction" can throw you off here a little.

-

In mathematics that is the identity element 0 for vector addition, and is a key object in the definition of a vector space.

Physically, if $(0, 0, 0)$ is the position vector of some particle, then that just means it is located at the origin.

-
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9572470784187317, "perplexity_flag": "head"}