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 proof of why $\sum x_iy_i$ would equal $|x||y|\cos\theta$, we would need a visual interpretation of $\sum x_iy_i$ in the first place. Do you have one in mind? I don't. I think the $\sum x_iy_i$ comes from linearity ...
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 product which is always strictly positive for nonzero vectors and nought if either vector is nought.
I have to find the area of a triangle whose vertices have coordinates O$(0,0,0)$, A$(1,-5,-7)$ and B$(10,10,5)$ I thought that perhaps I should use the dot product to find the angle between the ...
I googled my question but couldn't find a direct formula for vector product in the search results. Assume that I have $ \overrightarrow {V_1} $ and $ \overrightarrow {V_2} $ vectors in shperical coordinates:
What is a mathematical explanation of the connection between: (1) projecting vector a onto vector b and multiplying the projected length of a with the length of vector b, and (2) the sum of the pro...
In finding the derivative of the cross product of two vectors $\frac {d} {dt} [\vec {u (t)}\times \vec {v (t)}]$, is it possible to find the cross-product of the two vectors first before differentiating?
Derive the formula for the cosine of the difference of two angles from the dot product formula Ask Question Asked 8 years, 7 months ago Modified 8 years, 7 months ago
