# 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.

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### Orthogonal vectors in 4D

Consider two 4D vectors: $v_1=(\cos\varphi_1\sin\theta_1\sin\psi_1,\sin\varphi_1\sin\theta_1\sin\psi_1,\cos\theta_1\sin\psi_1,\cos\psi_1)$ and $v_2$, this vectors are orthogonal $v_1 \cdot v_2=0$, I ...
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### Orthogonal projection of a vector on a subspace

I have to determine the orthogonal projection of the vector v=(2, 4, 2) on the subspace Span(v1, v2). I know that V=(v1, v2, v3) where v1=(1, 0, 1), v2=(5, 1, 1,) and v3=(4, -1, 0). So far I have ...
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### Apostol: How to calculate work by force field along intersection of sphere and cylinder.

This question is about line integrals in cartesian and cylindrical coordinates. It is based on the following problem from Apostol's Calculus, Volume II, chapter 10 "Line Integrals", section ...
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### Can a purely mathematical version of the right hand rule be given?

The right hand rule is a common convention for describing orientation of coordinates, used throughout physics. It's also used in the definition of the cross product. Is it possible to give a purely ...
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### Finding parametric form of a circle that is in a plane $x-2y+z=0$ with radius 1 and center at origin

Find a parametric form of a circle that is in a plane $x-2y+z=0$ with radius 1 and center at origin In the book they picked $\hat u =(2,1,0)$ (hat for unit vector) , did cross product with the plane ...
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### How do you find the components of another vector given the components of a known vector and the angle between them in 3D?

I am working on a crystallographic problem. I am creating a 2D cross-section or slice of a surface in particular crystallographic directions. (I have found the angles of the extrema with respect to ...
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### What should be the result of this Roto-translation? [closed]

Suppose I have a rotation matrix mat = | 1 0 0 | | 0 1 0 | | 0 0 1 | a translation vector vec = | 1 1 1 | and, I ...
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### $u_1, u_2$ is linearly independent if and only if the family $u_1 + u_2, u_1 − u_2$ is linearly independent.

I have this exercise where I want to check my solutions. Can someone help me? Let $u_1$ and $u_2$ be elements of $V$. If $1 + 1 ≠ 0$ in $K$, then the family $u_1, u_2$ is linearly independent if and ...
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