5
votes
4answers
2k views

Why does cross product give a vector which is perpendicular to a plane

I was wondering if anyone could give me the intuition behind the cross product of two vectors $\textbf{a}$ and $\textbf{b}$. Why does their cross product $\textbf{n} = \textbf{a} \times \textbf{b}$ ...
1
vote
2answers
93 views

Given $u=(-2,5,3)$ find a unit vector $v$ s.t $|u\times v|$ is maximal, and then a unit vector $w$ s.t $|(u\times v)\cdot w|$ is minimal

This is a similar question to the one I have posted before. The problem is as in the title: Given $u=(-2,5,3)$ find a unit vector $v$ s.t $|u\times v|$ is maximal, and then a unit vector $w$ s.t ...
2
votes
3answers
7k views

What is the general formula for calculating dot and cross products in spherical coordinates?

I was writing a C++ class for working with 3D vectors. I have written operations in the Cartesian coordinates easily, but I'm stuck and very confused at spherical coordinates. I googled my question ...
1
vote
3answers
484 views

Cross product and dot product

What's the easiest way to understand and prove that $A \cdot B \times C = C \cdot A \times B $ ?
2
votes
1answer
106 views

Vector question, solving $r\wedge a=b$ and $r\wedge c=d$, with conditions

I am stuck on the following Show that the vector equation $r\wedge a=b$ has a solution $$r=\lambda a + \frac {a \wedge b}{|a|^{2}}$$ Show that the vector $r\wedge a=b$ and $r\wedge c=d$, with ...