# Tagged Questions

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### How to generate an ordered list of vertices of a cube from a face and a normal vector

Consider a cube with faces we'll call "left", "right", "front", "back", "top" and "bottom". The cube can be described by $0 \le x,y,z \le 1$. To name the faces, we'll say $x$ extends to the right, ...
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I want to find the exact sine between two vectors in 3-dimensional space. Data: $x$: vector $y$: vector $z = \Vert x \times y \Vert$ I have tried this: $$\sin \alpha = \frac{\Vert z\Vert}{( ... 6answers 5k views ### Is the vector cross product only defined for 3D? Wikipedia introduces the vector product for two vectors \vec a and \vec b as$$ \vec a \times\vec b=(||\vec a||||\vec b||\sin\Theta)\vec n $$It then mentions that \vec n is the vector normal ... 1answer 111 views ### Vector question, solving r\wedge a=b and r\wedge c=d, with conditions I am stuck on the following Show that the vector equation r\wedge a=b has a solution$$r=\lambda a + \frac {a \wedge b}{|a|^{2}} Show that the vector $r\wedge a=b$ and $r\wedge c=d$, with ...
I'm trying to prove whether the followings statements are true or not. I would appreciate your help, as I'm not sure how to begin. Given: $u,x_n \in \mathbb{R}^3$ and for every $n$, let \$x_{n+1}=u ...