I think the cosine comes from the cosine rule and not the compound angle formula. Given 2 vectors $\vec {a}$ and $\vec {b}$ emanating from the same point. Given the angle between …

Jul 29, 2015 · In two dimensions, where we have "cosine" already defined, from trigonometry, one can show that the "dot product", defined in some other way, is equal to the lengths of the two …

Aug 9, 2020 · Personally, I like that formula better as a definition of the dot product, then $\sum x_iy_i$ is the "formula" (because it depends on coordinates). Anyway, in order to have a visual …

Oct 6, 2017 · This complex "dot product" is sometimes called a Hermitian form. This specific separate term serves as a way to make it clear that it might not comply with the usual …

Feb 15, 2015 · In cross product the angle between must be greater than 0 and less than 180 degree it is max at 90 degree. let take the example of torque if the angle between applied …

May 23, 2014 · The dot product tells you what amount of one vector goes in the direction of another. For instance, if you pulled a box 10 meters at an inclined angle, there is a horizontal …

Sep 7, 2017 · Which brings us to the second way of looking at the problem. We begin with an abstract inner product, i.e. a symmetric, billinear (so that it is distributive by definition) scalar …

Sep 17, 2013 · In particular, the dot "$\cdot$" is used in the first formula to denote the scalar product of two vector fields in $\mathbb R^3$ called $a$ and $b$, while in the second formula …

I'm searching to develop the intuition (rather than memorization) in relating the two forms of a dot product (by an angle theta between the vectors and by the components of the vector ). For e...

Dec 12, 2014 · I don't understand the difference between the dot product of two vectors and the scalar projection of a vector onto another one. To me it looks like they are both (geometrically) …