Geometric object with magnitude (length) and direction.

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2answers
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The resultant of two forces acting at any angle?

I am studying about forces as vectors. And they give me this equation: $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
4
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1answer
1k views

Uniqueness of Helmholtz decomposition?

Helmholtz theorem states that given a smooth vector field $\pmb{H}$, there are a scalar field $\phi$ and a vector field $\pmb{G}$ such that $$\pmb{H}=\pmb{\nabla} \phi +\pmb{\nabla} \times \pmb{G},$$ ...
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3answers
2k views

Direction of Magnetic force from a current running through a coil of wire

What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it? ...
8
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6answers
1k views

Quaternions and 4-vectors

I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity: $(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$ Is it ...
0
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2answers
339 views

vector cross products

Lets say you have a free particle in a rotating frame of reference with constant angular velocity $\mathbf{\omega}$. By free, I mean there are no real forces on it. Lets call the moving system ...
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2answers
671 views

Understanding weight on an inclined plane

I'm trying to solve a problem where I have an object resting on an inclined plane, with the angle of the plan being alpha, and the weight being w. I'm having trouble figuring out how I can calculate ...
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3answers
3k views

Vector product in 2 dimensions [closed]

If I have a vector A=4i+3j and B=5i-2j, how can I find the vector product AxB? I know that given the angle, its C=AB sin theta, but how can I solve this without the angle?
8
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3answers
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Physics of a skateboard ollie

Does anyone have a good explanation of the physics and vectors of force involved in the skateboarding trick the ollie (where the skater jumps and causes the skateboard to rise off the ground with ...
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3answers
1k views

Can vectors in physics be represented by complex numbers and can they be divided? [closed]

Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided. In ...
2
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3answers
811 views

negative vectors (eg velocity)

If you said someone had a velocity of -12mph and they were traveling north? Wouldn't it mean that they were traveling 12mph south? This is a quote from here: if something [object-x] moving to the ...
9
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5answers
2k views

How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?