# Thread:

1. ## dot vs. cross

What is the purpose of the dot product as opposed to the purpose of the cross product?

2. ## Re: dot vs. cross

Originally Posted by delgeezee
What is the purpose of the dot product as opposed to the purpose of the cross product?
the result of a dot product of two vectors is a scalar ...

work, a scalar quantity of energy, is the dot product of force and displacement vectors

$W = \vec{F} \cdot \vec{\Delta x}$

the result of a cross product of two vectors is another vector ...

torque, a vector quantity, is the cross product of radius and force vectors

$\vec{\tau} = \vec{r} \times \vec{F}$

try a google search ... you'll find many more examples and applications.

3. ## Re: dot vs. cross

Originally Posted by delgeezee
What is the purpose of the dot product as opposed to the purpose of the cross product?
There is a very simple answer and distinction between the two operations.
The dot product operation maps pairs of vectors to a scalar.
The cross product operation maps pairs of vectors to a vector.
{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.9345458149909973, "perplexity_flag": "middle"}