# Dot products

How can I make something like dot products tangible? Are there real life examples where dot products are used? This is for motivating students. Aware that we can test for orthogonality.
Thanks in advance for any replies. Really appreciate anyone taking time out to answer these questions.

I usually define it in terms of projections, that is the most tangible and powerful picture in my opinion. With that I mean that I define it as the length of the first vectors projection on the other vector times the other vectors length. Projections are extremely useful and very intuitive, you can come up with some real life examples yourself but if you want I could give examples.

you can project a vector onto another vector (find the "shadow" cast onto a vector by another vector), you can find the angle between vectors (A.B = ABcos(theta)), and work is defined using the dot product. also, the definition of flux is defined using the dot product (vector field dotted with surface vector.

These are just a few of the many applications of the dot product.

And of course the dot product is zero if two vectors are orthogonal, since A.B = ABcos(theta), as you mentioned.

chiro