# Tagged Questions

In $\Bbb R^3$, the cross product of two vectors $v$ and $w$ produces a vector $v \times w$ perpendicular to both. This tag is not meant for products in other mathematical contexts, such as products of groups (such as the [tag:direct-product]), sets (the Cartesian product), graphs, and so on.

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### vectors in $3$ dimensions such that $v+(v \times u)=u$

Let $i,j,k$ denote the usual three unit vectors in $\mathbb R^3.$ 1) Find all vectors $v \in \mathbb R^3$ such that $v+(v \times i)=j$. 2) Suppose vectors $v$ and $u$ belong to $\mathbb R^3$ and ...
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### Points defining plane - starting step? [closed]

If the points $P, Q, R$, not all lying on the same straight line, have position vectors $a, b, c$ respectively, show that $(a \times b) + (b \times c) + (c \times a)$ is a vector perpendicular to the ...
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### Bilinear form and cross product in hyperbolic geometry

I'm reading Patrick J. Ryan's Euclidean and non-Euclidean geometry, page 152. There is a bilinear form defined by $b\left( {x,y} \right) = {x_1}{y_1} + {x_2}{y_2} - {x_3}{y_3}$ on ${\mathbb{R}^3}$ and ...
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### In this situation, based on order of operations, would cross product happen first or dot product?

I got from wikipedia that the dot product is also referred to as the "scalar product" and that the cross product is also referred to as the "vector product". Can anyone confirm my inference on the ...
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### Find a plane defined by a point, a ray, and a vector starting from the point and parallel to another plane

I am trying to figure this out for implementation into a Graphics manipulator I've been trying to work out. I need to find a plane (a normal vector to the plane will suffice) and I know some of its ...
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### Question about cross product and tensor notation

I am a bit rusty on tensor algebra and calculus and may use some wrong terminology, but I know that the cross-product can be expressed in tensor notation with the aid of the ...
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### The formula for the magnitude of cross product, $\| u\times v \| = \| u \| \|v \| \sin \theta$ [closed]

Can someone show me a proof of the magnitude (length) of the cross product: $$\|u \times v \| = \| u \| \|v \| \sin \theta$$
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If you have two vectors, $A$ and $B$, then we can write the cross product as $A \times B$. Simplify the following expressions: $A \times (A \times (A \times B))$ $A \times (A \times (A \times (A \... 1answer 70 views ### Solving for first term in vector product I'm trying to solve a system of equations for a physics application I've been working on, and I'm down to one thing left that's stumping me. Essentially, I need to solve $$A \times B = X$$ where$A, ...
Let vectors $u,v,w \in R^3$ Prove that $u \times (v \times w)$ must be a vector that satisfies the vector equation $x=sv+tw$ where $s,t \in R$ I have no idea where to go with this one, any tips?