Vector Definition and 1000 Threads

Homework Statement Which of the following correctly describes the velocity vector in each case? 2. The attempt at a solution I got it wrong at first. My new attempt (I have a sneaking suspicion that I am missing something important): For the first picture: dtheta_1/dt<0 - the angle is...

Hello all, I have a theoretical question regarding subspaces. If V is a subset of a vector space, and we wish to show that V is a vector space itself, we need to show 3 things. Some references say we need to show: a) V is not empty b) V is closed under + c) V is closed under scalar...

Greetings, can somebody show me how to calculate such a term? P= X E² where X is a third order tensor and E and P are 3 dimensional vectors. Since the result is supposed to be a vector, the square over E is not meant to be the scalar product. But the tensor product of E with itself yields a...

I am looks at problems that use the line integrals ##\frac{i}{{2\pi }}\oint_C A ## over a closed loop to evaluate the Chern number ##\frac{i}{{2\pi }}\int_T F ## of a U(1) bundle on a torus . I am looking at two literatures, in the first one the torus is divided like this then the Chern number...

Mod note: Moved to Precalc section Homework Statement Find the midpoint of the vector AB[/B] A(3,2,5) B(1,3,2) Homework Equations Not sure The Attempt at a Solution I wrote each point in terms of the unit vectors, i,j,k then I subtracted the two, and divided by a 2.

$\textsf{write an equation for}$ $\textsf{ The plane through the point (3, 2, -5) and perpendicular to the x-axis}$ 4ok I know this goes thru $3$ on the axis and it is \parallel to the $yz$ plane so is it just $x=3$.

Homework Statement Part b and e. Homework Equations Flux = surface integral of B (dot) ds The Attempt at a Solution I just want to make sure that I have a good understanding of ds. ds is just the direction of the vector that is normal to our area that we are finding our flux throuhg...

Hi, In a demostration i found a change in order i can't understand. how can the differential pass in the beginning part? the only thing I'm sure is that "v" and "dr" are parallel

Hii, As we know, Scaler triple product is volume of parallelopiped constructed by its three sides. Similary, What is the physical significance and geometrical interpretation of Vector triple product ? Also, What are the application where we use such mathematics and why ? Regards, Rahul

Question: A car is moving north at 100km/h. An hour later it is moving east at 100km/h. Its average acceleration during this hour is: a) A vector pointing northeast b) A vector pointing southeast c) A vector pointing southwest d) A vector pointing east e) Zero Attempt: I confidently chose a) A...

Why is it difficult to find really challenging vector analysis problems (problems about Green's, Stokes' and Gauss' theorems in a Calculus 3 course) in Calculus books? Most of the problems are elementary, at least that's the impression I have(I could be wrong). Is it really difficult to...

How do I define a vector starting on the x-Axis at -d/2 ending at d/2 on the x-Axis?

I'm learning Differential Geometry on my own for my research in ML/AI. I'm reading the book "Gauge fields, knots and gravity" by Baez and Muniain. An exercise asks to show that "if \phi:M\to N we can push forward a vector field v on M to obtain a vector field (\phi_*v)_q = \phi_*(v_p) whenever...

$\textsf{Write a complete solution.}\\$ $\textit{ok Let A be the point (1,2,3) and O the origin (0, 0, 0). }\\$ $\textit{Consider the points P (x, y, z) such that AP · OP − OA · OP = 2 − |OA|2.}\\$ $\textit{Show that the set of all such points is a sphere, and find its center and radius.}\\$...

I want to know if i did this problem correctly! Problem: A projectile is traveling with velocity vector v = (30.00 m/s)i + (20.0 m/s)j when it experiences an acceleration of vector a = (-10.00 m/s^2)j. What is its velocity after 2.0 s? What is its speed after 2.0 s? My work: Vy = V0y - gt =...

Homework Statement A pole BC is supported by the cable AB as is shown in the figure. If the magnitude of the force applied on the point B is 70 lb, and the moment of this force about the x-axis is -763 lb ft, determine the pole lenght. I'LL ATTACH AN IMAGE SO YOU CAN SEE IT. Homework Equations...

$\textsf{Find the vector perpendicular to the plane PQR determined by the points}$ \begin{align*}\displaystyle &P(2,1,3), \, Q(1,1,2), \, R(2,2,1)\\ \end{align*} $$\textbf{ solution:}$$ \begin{align*}\displaystyle \vec{PQ}&=(1-2)i+(1-1)J+(2-3)k=&-i-k\\...

Who can make the most impressive, interesting, or pretty TikZ picture? This third challenge is to create a vector diagram. Such as used in geometric figures, or in physical diagrams with forces and velocities, or in state diagrams. For more impressive arrows, we might use the arrows tikz...

Or is it something separate that acts on a geometric space? So we know that the Euclidean space is a vector space. But is it geometric? I ask this because in group theory, the group elements are the operators acting on another set, but clearly we see that this doesn't mean that the group...

Homework Statement I attempted to solve the problem. I would like to know if my work/thought process or even answer is correct, and if not, what I can do to fix it. I am given: Calculate the divergence of the vector field : A=0.2R^(3)∅ sin^2(θ) (R hat+θ hat+ ∅ hat)Homework Equations [/B] The...

Homework Statement A stone is thrown at 25m/s and at 37 degrees above the horizontal from a 20m high building. Take g=10m/s2 Let D be the displacement vector from launch point on top of the building to landing point on the ground, and v be the velocity vector on impact, what is the angle...

Homework Statement 1. Calculate the electric field at field point 3i + 6j created by a 5.50uC electric charge at 13i + 8j 2. Calculate the electric force on an electron at field point 3i + 6j and in the same electric field calculated for the prior problem. Homework Equations The Attempt at a...

In mechanics, a vector is represented by complex number (x + i y). Is there a simple/intuitive explanation as to why the y component is multiplied by i , which is equal to square root of -1 ? ; In this case, did it have to be of value sqrt(-1) ? or is "i" used to keep x and y separate and not...

Homework Statement The Trump's wall is so weak that has to be supported by two cables as is shown in the figure. If the tension over the cables BD and FE are 900 N and 675 N respectively. (I'LL UPLOAD AN IMAGE OF THE PROBLEM SO YOU CAN SEE IT) Homework Equations τ = r χ F Mo = r χ F The...

Could someone please provide a diagram of all the forces acting on the plane, and explain why the answer is E? This is from the 2014 F=MA exam. Thanks, blueblast

Say we have a matrix L that maps vector components from an unprimed basis to a rotated primed basis according to the rule x'_{i} = L_{ij} x_{j}. x'_i is the ith component in the primed basis and x_{j} the j th component in the original unprimed basis. Now x'_{i} = \overline{e}'_i. \overline{x} =...

Homework Statement A quadrangular pyramid OABCD with square ABCD as the bottom. OA = 1, AB = 2, BC = 2 Also, OA perpendicular to AB, OA perpendicular to AD. Question 1 : Find the inner product \overrightarrow {OA}.\overrightarrow {OB} and the size of the cross product |\overrightarrow...

Homework Statement Find the divergence of the function ##\vec{v} = (rcos\theta)\hat{r}+(rsin\theta)\hat{\theta}+(rsin\theta cos\phi)\hat{\phi}## Homework Equations ##\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^2v_r)+\frac{1}{r sin\theta}\frac{\partial}{\partial...

I am having trouble with this proof. I just need a step in the right direction. Let u and v be vectors. (u+v)*(u-v)=0, then IuI=IvI I have to use properties of the dot product. I started off by combining both using this property u*(v+w)=u*v+u*w (u,v,w are vectors) I got lost in all of my...

Homework Statement F =(70N, 57.1∘counterclockwise from positive y−axis)[/B] Find the vector components of F Homework Equations Sin and Cos of the angle[/B]The Attempt at a Solution x is component is 38 and y component is 58 how does the angle being counterclockwise affect my answer? The...

<Moderator's note: Moved from a technical forum and therefore no template.> Homework Statement A proton (q = 1.60 x 10-19) is in a uniform, 0.500 T magnetic field. This proton has velocity components vx = 1.50 x 105, vy = 0, and vz = 2.00 x 105 m/s. Find the force on the proton at t=0. 2...

Hello! I am not sure I understand the idea of vector field on a manifold. The book I read is Geometry, Topology and Physics by Mikio Nakahara. The way this is defined there is: "If a vector is assigned smoothly to each point on M, it is called a vector field over M". Thinking about the 2D...

Hello all! I usually don't like to ask for help... But this is the first week of courses and I'm already stumped on a homework question... 1. Homework Statement So the question states: Find the work by the force F = x^i + xy^j. If the object starts from the origin (0,0), moves along the...

Hello, Im creating a physics simulator and I am struggling to expand my collisions from 2D to 3D. In 2D the velocity only changes parallel to the line of center so I presume this is the same for 3D.I can get a Cartesian equation of line but I am not sure how to get the velocity component...

Homework Statement [/B] Sketch in a third vector, C, whose magnitude and direction are such that A+B+C=0. Vectors A and B both have a magnitude of 5 and form a 30 degree angle (image attached).Homework Equations [/B] How do I go about this question? I have no idea how to start or what to...

Suppose we have two vectors ##a = [1,2,3]## and ##b = [4,5]##. I want to construct the matrix of products, i.e. $$ \begin{bmatrix} 1\cdot 4 && 1\cdot 5\\ 2\cdot 4 && 2\cdot 5\\ 3\cdot 4 && 3\cdot 5 \end{bmatrix} = \begin{bmatrix} 4 && 5\\ 8 && 10\\ 12 && 15 \end{bmatrix} $$ Does anyone know an...

I have been reading Ramamurti Shankar's book "Principles of Quantum Mechanics". The author, in the first chapter, briefs out the elementary mathematics required for quantum mechanics. Now, the author has described vector spaces, and made it very clear that only arrowed vectors that one studies...

Hello, everybody! I would really appreciate if someone could help me understand how to solve the following two tasks. I am not sure whether my translation is correct, so if, by any chance, you know a more appropriate terminology, please let me know. I am not fluent in writing matrices here on...

Homework Statement I start walking. The first leg of my trip I walk 65 meters at 5 degrees south of east. The second leg of my trip I walk 75 meters at 18 degrees north of east. The final leg of my trip I walk 95 meters at 69.5 degrees north of west. Choose the coordinate system so that x is...

Homework Statement What are the associated peak amplitudes of the E and H fields if sunlight has a maximum intensity of 1400 W/m2 on the earth’s moon? Homework Equations I = <s> = 1/2 c ε0E2The Attempt at a Solution I = <s> = 1/2 c ε0E02 1400 = (1/2)(3*108)(8.85*10-12)(E02) 1400 /...

Homework Statement show that points P, Q and R are in a straight line P (1, -3, 4) Q ( 2, 2, 1) R (3, 7, -2) and find the vectors ## \vec{PQ} ## and ## \vec{QR} ## Homework EquationsThe Attempt at a SolutionIn proving that the points are in a straight line, we might be able to use dot product...

Homework Statement Hi everyone. We were discussing conservation of angular momentum as a consequence of rotational invariance in class. There was one point where we needed to compute the change in a vector A when the coordinate frame is rotated by angle Δ(Φ). Homework Equations The teacher...

Let say a car move with constant speed to the right. Can I say the acceleration is zero and is directed to the right? Or we can not assign certain direction to a zero-magnitude vector because I can also say that the car has zero backward acceleration (directed to left)? Thanks

The question: The line L1 has equation r = \left( \begin{array}{ccc}4 \\-1 \\0\\\end{array} \right) + t\left( \begin{array}{ccc}1 \\1 \\-1\\\end{array} \right) , and point A has coordinates (4, 8, -3). Find the coordinates of point B on L1, such that \overrightarrow{AB} is perpendicular to...

particles in plane polar coordinates r = rcosθ i + rsinθ k F = Fer + Feθ ∂r/∂r =|∂r/∂r|er = (cos2θ + sin2θ)½er = er why ∂r/∂θ =|∂r/∂θ|eθ = (r2cos2θ + r2sin2θ)½eθ = reθ I understand that ∂r/∂θ = -rsinθ + rcosθ but why ∂r/∂θ = (r2cos2θ + r2sin2θ)½eθ

Homework Statement I have a curve $$\Psi(t) = \hat h_\alpha$$ where the coordinates are $$\alpha=0, \beta=t$$ and $$\gamma=t$$ in the system. Additionaly $$x=\sqrt2 ^\alpha \cdot(sin\beta-cos\beta)\cdot \frac{1}{cosh\gamma}$$ $$y=\sqrt2 ^\alpha \cdot(cos\beta+sin\beta)\cdot...

When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...

From my drawings it seems to be half of hemisphere. Am I right? How can I solve this task? Determine the flux of the vector field $$ f=(x,(z+y)e^x,-xz^2)^T$$ through the surface $Q(u,w)$, which is defined in the follwoing way: 1) the two boundaries are given by $$\delta...

I know that vector spaces have more structure as they are defined over fields and that modules are defined over rings. But it's hard to think of a situation where a using a ring clearly backfires. Is it just because a ring doesn't have an inverse for the second operation? For a module over Z...

I am an engineering major at Los Angeles Pierce community college. I have been for the last years working 40 hours a week in order to sustain and put myself through community college. After I transfer, I don't plan on working. Now, each semester due to my work schedule and life happening, I can...