# Questions tagged [vectors]

Use this tag for questions and problems involving vectors, e.g., in an Euclidean plane or space. More abstract questions, might better be tagged vector-spaces, linear-algebra, etc.

385 questions
5k views

### What is the logic/rationale behind the vector cross product?

I don't think I ever understood the rationale behind this. I get that the dot product $\mathbf{a} \cdot \mathbf{b} =\lVert \mathbf{a}\rVert \cdot\lVert \mathbf{b}\rVert \cos\theta$ is derived from ...
43k views

### Is the vector cross product only defined for 3D?

Wikipedia introduces the vector product for two vectors $\vec a$ and $\vec b$ as $$\vec a \times\vec b=(\| \vec a\| \|\vec b\|\sin\Theta)\vec n$$ It then mentions that $\vec n$ is the vector normal ...
95k views

### What does the dot product of two vectors represent?

I know how to calculate the dot product of two vectors alright. However, it is not clear to me what, exactly, does the dot product represent. The product of two numbers, $2$ and $3$, we say that it ...
4k views

### Cross product in higher dimensions

Suppose we have a vector $(a,b)$ in $2$-space. Then the vector $(-b,a)$ is orthogonal to the one we started with. Furthermore, the function $$(a,b) \mapsto (-b,a)$$ is linear. Suppose instead we have ...
6k views

### Why is cross product defined in the way that it is?

$\mathbf{a}\times \mathbf{b}$ follows the right hand rule? Why not left hand rule? Why is it $a b \sin (x)$ times the perpendicular vector? Why is $\sin (x)$ used with the vectors but $\cos(x)$ is a ...
23k views

### Is arrow notation for vectors “not mathematically mature”?

Assuming that we can't bold our variables (say, we're writing math as opposed to typing it), is it "not mathematically mature" to put an arrow over a vector? I ask this because in my linear algebra ...