# Tagged Questions

Geometric object with magnitude (length) and direction.

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### Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
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### Finding resultant and direction of resultant

In this question- A motorboat is racing towards north at 25km/h and the water current in that region is 10km/hr in the direction of 60 degree east of south. Find the resultant velocity of the boat....
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### Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?

According to some physicist at KIT it is usual to write the following when using pen and paper: whereas in typeset texts you write $\nabla$. Is that true? Are there sources for this convention?
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### Can a vector be defined by invariance of some algebraic operation to translations rather than rotations?

Every physics book I've come across defines a vector as an n-tuple of numbers that can be combined via an inner product that's invariant to rotations. Is it possible to instead define a vector via ...
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### Flow rate is calculated only using the parallel component of the velocity vector

Flow rate is calculated using only the parallel component of the velocity vector to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular ...
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### The work done by running in a rectangle

This may be quite off-topic but please help me. Is there any work done when I run in a rectangle? I thought that the answer should be no. But my teacher says that we should calculate each side ...
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### We need to find unit vector along the reflected ray [closed]

A ray of light on a plane mirror comes along a vector $i+j-k$ The normal on incidence point is along $i+j$ we need to find unit vector along the reflected ray. I am not able to solve and draw the ...
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### Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
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### Vectors and motion in a plane [closed]

A particle travels with speed $50 m/s$ from the point $(3,-7)$ in the direction $7i-24j$ . Find its positional vector after 3 seconds. My approach: It has travelled a distance of 150m in the ...
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Say we have three forces $F_1, F_2, F_3$, such that $$F_1 + F_2 - F_3 = 0\hspace 10mm (1)$$ And let us say that $F_1$ and $F_2$ have the same direction and magnitude, and that $F_3$ has double the ...
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### Component of force field tangent to a curve

I recently had to solve the following problem: A force $F=10\hat x- 8\hat y$ is applied to an object that is constrained to travel towards increasing values of x along the path defined by $y=x^2$ ...
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### Vector Nature Of Angular Velocity

I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help ...
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### Proving that force satisfies the laws of vector addition [duplicate]

A vector quantity has both magnitude and direction. So, for any physical quantity to be a vector, it should have a direction and a magnitude. Though this is a necessary condition for any quantity to ...
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### Why is speed defined as coordinate derivative over proper time rather than observer's time in STR?

In special theory of relativity, why is 4-velocity defined as: $$u^\mu = \frac{dx^\mu}{d\tau}$$ and not as $$u^\mu = \frac{dx^\mu}{dt}$$ where ${\tau}$ is proper-time and t is time in some ...
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### Elemetary Rotations -imagining differential rotations - intitutive proof of such rotations being vectors

I was reading and extract from "Fundamentals Laws of Mechanics", 1980, by I.E Irodov, § 1.2. 'Kinematics of a Solid' and came across this insane text where the author asks me to imagine a 'solid ...
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### Am I wrong about the right hand grip rule?

The right hand grip rule (also known as right hand screw rule) tells you the direction of a magnetic field due to a current. If you point your thumb in the direction of the current, your fingers will ...
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### How should speed be expressed in Frenet-Serret frame of reference? [closed]

I'm looking for the equation of motion of the ball on a vertical plane with a cylindrical profile. I guess that means I have to use the frame of reference of Frenet-Serret here. Why is the speed of ...
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### Bounced ray angle of normal direction? (SOLVED) [closed]

TL;DR whats the position of C. I'm currently programming something and for some reason I having problem figuring this one out, imagine having a ray / or ball bouncing (without mass or gravity etc) ...