Why is the dot product of two vectors defined the way in which it is?
22182
why don't we define vector multiplication component-wise?
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
47598
Motivation behind the definition of tangent vectors
123392
How does $cos(x) = \frac{\vec{v} \cdot \vec{w}}{|\vec{v}| \cdot |\vec{w}|}$ make sense?
76510
vector identity for triple scalar product
89517
Do four dimensional vectors have a cross product property?
29018
Do the BAC-CAB identity for triple vector product have some intepretation?
40478
If $C$ commutes with certain matrices $A$ and $B$, why is $C$ a scalar multiple of the identity?
13658
Distinction between vectors and points
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
103142
Question on equivalence of inner product
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
2743
Dot Product and Cross Product: Solving a set of Simultaneous Vector Equations
151402
What is the difference between a vector and its transpose?
6898
Is the vector cross product only defined for 3D?
73242
Simplify vector expression - is there something like "Factor" for vectors, dot products etc.?
106319
Can we divide two vectors?