# Dot Cross and Triple Products

> The dot product, cross product, and scalar triple product each serve a distinct purpose. The dot product provides a scalar value that measures the alignment of two vectors, while the cross product produces a new vector perpendicular to the original two. The scalar triple product, also a scalar, represents the volume of the parallelepiped formed by the three vectors. The interactive demo enhances this understanding by transforming the static problem into a dynamic learning tool. By allowing users to change input values and instantly see the results, it bridges the gap between abstract, symbolic math and concrete, numerical outcomes. This real-time feedback loop helps to solidify the theoretical concepts and makes the learning process more intuitive and engaging.

### :clapper:Narrated Video

{% content-ref url="../animated-results/algebraic-cross-product-vs.-geometric-lie-bracket" %}
[algebraic-cross-product-vs.-geometric-lie-bracket](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/algebraic-cross-product-vs.-geometric-lie-bracket)
{% endcontent-ref %}

### :paperclip:IllustraDemo

{% content-ref url="../illustrademo/visualizing-dot-cross-and-triple-products" %}
[visualizing-dot-cross-and-triple-products](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/illustrademo/visualizing-dot-cross-and-triple-products)
{% endcontent-ref %}

### :scarf:Example-to-Demo

{% content-ref url="../example-to-demo/algebraic-and-differential-properties-of-vector-fields-ad-vf" %}
[algebraic-and-differential-properties-of-vector-fields-ad-vf](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/example-to-demo/algebraic-and-differential-properties-of-vector-fields-ad-vf)
{% endcontent-ref %}

### :hammer\_pick:Compound Page

{% embed url="<https://viadean.notion.site/Dot-Cross-and-Triple-Products-DCT-24b1ae7b9a3280ea9075e6304c7236d3?source=copy_link>" %}