why is $ \vec u \bullet \vec v = u_1v_1 + u_2v_2$?
117313
What is the dot product and why do we need it?
140464
Is Gauss's law wrong, or is it possible that $\int_s{\vec E} \cdot d\vec{s}=0$ does not imply $\vec E = 0$?
15199
What is the use of the Dot Product of two vectors?
144097
eigenvalues and eigenvectors of $vv^T$
92377
Why is $\mathbf{B}$ a pseudovector?
81375
Why does $V(I(S))=\overline{S}$?
90287
How to derive $[x_i, F(\vec p)] = i \hbar \frac {\partial F(\vec p)}{\partial p_i}$
142821
Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
56355
What does the equation $P=\vec{F}\cdot \vec{v}$ really mean?
16644
Why does cancellation of dots $\frac{\partial \dot{\mathbf{r}}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$ work?
35564
Prove that $u\cdot v = \frac{1}{4}||u+v||^2 - \frac{1}{4}||u-v||^2 \forall u,v \in \mathbb{R^n}$
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
116821
Does velocity add like vectors?
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
51253
Graphical intuition behind directional derivative interpreted as a(∂f/∂x)+b(∂f/∂y), where  is directional vector of unit length?
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$