# Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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### Why is the tension $\vec T$ downwards in the system?

Link to video Doubt: At pulley $A$, consider the free-body diagram. Why is the tension, $\vec{T}$, in both hands downwards? I know $\vec{T}_2$ is upwards since it is the force acting upwards in ...
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### Flight time of spherical bullet fired horizontally versus dropped vertically / effect of crosswind on spherical car

Would a spherical bullet fired horizontally from a musket stay aloft longer than a spherical bullet dropped from the same height? I know two similar questions have been asked (Will a bullet dropped ...
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### The sign of $d\mathbf{r}$ when integrating the universal gravitational force in order to define gravitational potential energy [duplicate]

I am trying to find gravitational potential energy by integrating the gravitational force: $$\mathbf{F}(\mathbf{r}) = - \ G \frac{Mm}{|\mathbf{r}|^2} \ \hat{\mathbf{r}}$$ where $\mathbf{r}$ is the ...
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### If the vector $\vec{A} = 2\hat{i}+4\hat{j}$ and $\vec{B} = 5\hat{i}+p\hat{j}$ are parallel to each other, the magnitude of $\vec{B}$ is? [on hold]

If the vector $\vec{A} = 2\hat{i}+4\hat{j}$ and $\vec{B} = 5\hat{i}+p\hat{j}$ are parallel to each other, the magnitude of $\vec{B}$ is____________ how to solve it?
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### Is my understanding of vectors correct?

I recently learned that a vector in mathematics (an element of vector space) is not necessarily a vector in physics. In physics, we also need that the components of the vector on a coordinate ...
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### Why are products of vectors just the way they are, and not the other way around? [migrated]

The scalar product and vector product of two vectors $\vec{A}$ and $\vec{B}$ are $AB\cos\theta$ and $AB\sin\theta\space\hat{\eta}$, respectively. They could have been the other way around—that is to ...
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### Why does the Cross Product have to be perpendicular to the two vectors? [migrated]

I understand that the cross product of two vectors equals the area of the parallelogram. But I don't understand why multiplying the two vectors gets you a vector perpendicular to the two vectors.
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### How to prove a 4D vector is a 4-Vector?

This is a fairly open ended question. Given a set of 4 Components, that is, a 4D Vector, what is the process for determining rather or not it is a "4-Vector" as defined in special relativity? I want ...
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### Intuition of 2D Velocity Vectors [duplicate]

I understand 2D vectors in terms of displacement. For example, Bob moves 3m to the east and 4m to the north, the total change in position (displacement) equals 5m to the north east. But I don't ...
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### Geometry with differential angles

In the solution to a problem, the author considers the normal force provided by an arc length of string with a differential subtended angle size, $\textrm{d}\theta$. The author reasons that this ...
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### Order of positions of tensor/vector components in an inner/outer product

Show that if $T_i$ are the components of covariant vector T, then $S_{ij}=T_iT_j-T_jT_i$ are the components of a skew-symmetric covariant tensor S. The question is whenever working with equations of ...
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### Basis of 2D motion analysis

The basic argument for analysing 2D motion is that if we have a projectile we can break its 2D motion into 2 1D motions along 2 perpendicular axes. The motions along these axes and their corresponding ...
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### Appropriate Vector Diagram for Force

Which of these two vector diagrams is befitting for illustrating exerted force?
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### Wavelength scalar/vector ambiguity?

I have seen the de Broglie relation for wavelength written as $\lambda$ = $\frac{h}{\gamma(\vec{v})m_o\vec{v}}$ I know wave propagation in the one - dimensional case makes wavelength a scalar, as ...
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### Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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### Is this Question correct? Newtonian Motion - Relative Motion of Rain

There is a question in a textbook which states: "A cyclist is riding north at 12km/h when it starts to rain. The rain appears to be falling towards her at an angle of 10 degrees relative to the ...
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### How do you calculate the speed of air when it fills a vacuum of 1 cm³?

At different heights, atmospheric pressure is different. If a vacuum was created of say 1 cm³, how would i calculate the velocity of air filling it back in. The adjacent layer of air would obviously ...
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### Prove acceleration in orbit with newtons second law

I want to prove that the acceleration in a orbit at a given point r=(x,y) is $a=-\frac{GM}{R^3}r$ (My professor said this can be proven by newtons second law, but he never explained in detail how). I ...
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### Work-Kinetic energy theorem derivation

So I came across this derivation in the book Classical Mechanics by Herbert Goldstein. I don't follow from the second step onwards. I understand that there's a dot product, but how do you compute it? ...
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### Is there a scalar acceleration?

Distance is paired with Displacement and it seems to be a bigger idea than just the magnitude of Displacement. Speed is paired with Velocity. I have always thought that there is not such pairing with ...
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### Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
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### Direction of cross product of two vectors [duplicate]

Are there several ways to find the direction of a×b other than right hand thumb rule?
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### Question on notation for the inner product of complex vectors [duplicate]

Regarding the wiki: https://en.wikipedia.org/wiki/Sesquilinear_form#Hermitian_form you can see that the wiki states that physics defines the inner product for complex vectors as: \langle \, \...
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### Where does 4N and 3N goes in this diagram?

Two forces of 3 N and 4 N are acting at a point such that the angle between them is 60 degrees. Find the resultant force. I successfully draw diagram for above sentence: But I am confused which one ...
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### Why are the vectors canceled out in this scenario for angular momentum of a particle?

I have a study guide for our next test, and I'm trying to understand the professors answer but I don't understand why i^ * i^ = 0? Here is his work, Why do we know that the P Vector is on direction ...