Vectors Definition and 1000 Threads

I've been looking at various online sources for relativity and have some confusion about "dual vectors." I'm hoping for some very basic information/examples from physics, not abstract mathematical concepts from the field of vector spaces. 1. In addition to the vector/dual vector distinction...

Homework Statement A bird flying in the air accelerates 2.82 m/s2 north for 4.11 seconds. the final velocity of the bird is 9.09 m/s [east]. What was the initial velocity of the bird? Homework Equations vf=v0+a*t v(average)=(v0+vf)/2 v=d/t d=v0t +½at2 tanθ=opp/adj The Attempt at a Solution...

Hello, I am an undergrad currently trying to understand General Relativity. I am reading Sean Carroll's Spacetime and Geometry and I understand the physics (to a certain degree) but I am having trouble understanding the notation used as well as the ideas for tensors, dual vectors and the...

I have no clue how to decode this question or do it but I was given the vectors S=[1 1 0] and T=[-1 0 1] and asked to determine whether or not they are in the column space of ABC when A, B and C are 3x3 matrices. My prof hinted to "think of rank and nullity", can someone please point me in the...

I know that a dot product of 2, 2 dimension vectors a, b = (ax * bx) + (ay * by) but it also is equal to a*bCos(θ) because of "projections". That we are multiplying a vector by the 'scalar' property of the other vector which confuses me because that projection is in the direction of the...

Given the following vectors: how can i determine that Θ = Δp/p ? I can understand that p + Δp = p' but nothing arrives from this. Any help is welcome!

Hello guys, I have a question regarding commutators of vector fields and its pushforwards. Let me define a clockwise rotation in the plane \,\phi:\mathbb{R}^2\rightarrow\mathbb{R}^2 \,.\; [\,\partial_x\,,\,\partial_y\,]=0 \,, \;(\phi_{*}\partial_x) = \partial_r and \,(\phi_{*}\partial_y) =...

I isolated the member ABC and drew the free body diagram: α is then calculated using inverse tan: Tan-1=(6.25+15)/50=23.03 Then force of member BD on the joint can be found by sum of all moments around point A. Then Ax is calculated which is equal to BD×Cos(α)=235.2×Cos(23.03) Ax=216.48...

Hi everyone! I have a problem with one thing. Let's consider the Lorentz group and the vicinity of the unit matrix. For each ##\hat{L}## from such vicinity one can prove that there exists only one matrix ##\hat{\epsilon}## such that ##\hat{L}=exp[\hat{\epsilon}]##. If we take ##\epsilon^{μν}##...

Homework Statement Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that |u|=√2, |v|=√3, u is perpendicular to v, w=u×v. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ The Attempt at a Solution [/B] Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...

Homework Statement Let a and b be non-zero vectors in space. Determine comp a (a × b). Homework Equations comp a (b) = (a ⋅ b)/|a| The Attempt at a Solution [/B] comp a (a × b) = a ⋅ (a × b)/|a| = (a × a) ⋅b/|a| = 0 ⋅ b/|a| = 0 Is this the answer? Or is there more to it?

this is what is given so by addition $$\begin{bmatrix}x_1\\y_1\\5z_1\end{bmatrix} \oplus \begin{bmatrix} x_2\\y_2\\5z_2 \end{bmatrix} = \begin{bmatrix} x_1+x_2\\y_1+y_2\\5z_1+5z_2 \end{bmatrix} = \begin{bmatrix} X\\Y\\10Z \end{bmatrix}$$ uhmmmm really?

Problem: Dr. L and his cat Kepler are coming home from fishing. They ended their trip on the south bank of a river, directly across a 1200 m wide river, from where Caroline was going to pick them up on the north bank. They are in identical boats that can travel at 4 m/s (Vb). The river is...

Hello, I get that both polar unit vectors, ##\hat{r}## and ##\hat{\theta}##, are unit vectors whose directions varies from point to point in the plane. In polar coordinates, the location of an arbitrary point ##P## on the plane is solely given in terms of one of the unit vector, the vector...

Homework Statement Homework EquationsThe Attempt at a Solution I have found expressions for the unit vectors for cylindrical coordinates in terms of unit vectors in rectangular coordinates. I have also found the time derivatives of the unit vectors in cylindrical coordinates. However, I am...

Homework Statement a particle's position is the vector r=(ct^2-2dt^3)i+(4ct^2-dt^3)j where c and d are positive constants. find the expression for the x-component of the velocity (for time t>0) when the particle is moving in the x-direction. you should express your answer in terms of variables...

Homework Statement P(3, 0, 3), Q(−2, 1, 5), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR Homework Equations A = \frac{1}{2}|\vec{AB}\times\vec{AC}| Source...

Homework Statement A tent with no bottom stands in a terrain. The tent has three rods that are gathered in T = (1,1,4). The tent bars stands in the points A = (0,0,0), B = (3,1,1) and C = (- 1,3,2). The tent must be supported by an additional rod which is in a point D and attached to T. The rod...

I am told: "A differential p-form is a completely antisymmetric (0,p) tensor. Thus scalars are automatically 0-forms and dual vectors (one downstairs index) are one-forms." Since an antisymmetric tensor is one where if one swaps any pair of indices the value of the component changes sign and 1)...

I'm having trouble finding textbook material on nonlinear functions on vectors. Just as I could define a function ##f## such that: $$f(x) = cos(x)$$ I'd like to write something like: $$f(\vec{x}) = \begin{pmatrix} f_1(x_1) \\ f_2(x_2) \\ ... \\ f_n(x_n) \end{pmatrix} $$ where ##f_i## is...

Homework Statement [/B] Hopefully this is in the correct section I looked around for others but this seemed like the right one. Find the scalar, vector, and parametric equations of the plane that passes through the points P(1,0,4), Q(3,1,-6), and R(-2,3,5). Homework EquationsThe Attempt at a...

I know how to find the cos(theta) between two vectors but I do not know how to find the sin(theta). vector w=i+3j vector v=<5, 2>

Hi there, I have another one for you (Blush) How can I efficiently determine if the angle between 2 vectors is positive or negative... Take a look at this example drawing: Known are the xy coordinates of 2 adjoining vectors, (I also have calcullated the 360 deg angle relative to the x-axis...

Tomorrow is my math test and I'm going over the study guide: I have vector U=<1, 3> and vector V=<5, 2> It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)? I already know how to find the missing angle for cos(theta) but we never covered how...

I don't understand a good portion of the non-algebraic math behind much of the physics in my first semester college class. I understand everything with algebra, and can solve all problems, but I don't understand the relationships with vector cross/dot products, calculus derivations, DE, etc...

I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ... I need help in order to fully understand Tu's section on tangent vectors in \mathbb{R}^n as derivations... In his section on tangent vectors in \mathbb{R}^n as derivations, Tu writes the following: In the above...

<Moderator's note: Moved from a technical forum and thus no template.> Let there be two vectors, u and v. Whose magnitudes are constant u = [a, b] v = [x, y] Define c = ||u|| and k = ||v|| Now sum the vectors: w = u + v = [a, b] +[x, y] = [a+x, b+y] Now find ||w|| ||w|| =√(a+x)2+(b+y)2...

I was reading Fundamentals of Inket Printing and it said the following: "The surface tension in a liquid causes a force to act in the plane of the free surface perpendicularly to a free edge in that surface." Can someone explain to me what this means? What's the direction of the force? I have...

Hey! :o We have the basis $B=\left \{\begin{pmatrix}1 \\ 1 \\ 1\end{pmatrix},\begin{pmatrix}2 \\ 1 \\ 0\end{pmatrix}, \begin{pmatrix}1 \\ 2 \\ 1\end{pmatrix} \right \}$ of $\mathbb{R}^3$ and the vector $v$ can we written as a linear combination of the elements of the basis as follows...

Hi! I was trying to understand circular motion and came across two problems. I would really appreciate if you could help me with those. Question 1: In the picture below let's assume that the angle θ is 1 radian, i.e. 57.3°, radius is 1 m. It would mean that the length of arc AB is also 1 m...

Homework Statement I'm working through an example with motional EMF and I'm having trouble understanding the directions of vectors so that I can apply induction law. The magnetic circuit seems complex because the circuit is used to analyze other situations but the air gap 3, the coil 3 and the...

Hi. The book I am using gives the following equations for the the Lorentz transformations of contravariant and covariant vectors x/μ = Λμν xν ( 1 ) xμ/ = Λμν xv ( 2 ) where the 2 Lorentz transformation matrices are the inverses of each other. I am trying to get equation 2...

Homework Statement (Translating from a Polish high school textbook, so if anything is unclear please let me know). An object moves on a trajectory described by the parabola ##y=\frac{1}{2\lambda}x^2## such that the ##x## component of its velocity is constant and equal to ##v_0##. The...

Homework Statement Prove that $$\bf{ a \times ( b \times c ) = \phi [ b(a \bullet c) - c(a \bullet b) ]} $$ for some constant phi Homework EquationsThe Attempt at a Solution So I have used the unit vectors i, j, and k and found out that phi = 1. With the main part of the proof, we are not...

I'm learning APL and this is how a vector is defined https://tryapl.org: All data resides in arrays. An array is a rectangular collection of numbers, characters and arrays, arranged along zero or more axes. We can use more specific terms for some arrays, like a single number is a scalar, a list...

For example, does this always hold true? M_ab = v_a × w_b If not, where does it break down?

Homework Statement I know how to approach this problem; however, I'm just confused as to why we consider that R^2 is a vector space over the field R, and not Q or any other field for this question? Standard basis vectors: e_1, e_2 or i,j

Homework Statement A man drives a car starting 5.00 km due West from the line marking the Eastern time zone. He travels at 30 m/s along a straight road that runs in a direction E 30° N. How much time does it take the man to get to the Eastern time zone? (The man must travel along the road: no...

Homework Statement The velocity of an airplane is 425 km/h, in a direction of 40 degrees north of east. The wind is blowing at a velocity of 75 km/h northward. A. What is the resultant velocity of the plane? B. How long does it take for the plane to make a displacement of 2000 km? Homework...

Homework Statement In a finite-dimensional vector space, the length of every linearly independent list of vectors is less than or equal to the length of every spanning list. It's quite long :nb), hope you guys read through it. Thanks! :smile: Homework Equations N/A The Attempt at a Solution...

hi. if I know how to convert coordinates from a system to cartesian system, then how can I find basevectors of that coordinatesystem? Is it possible that basevectors are different in different points(with different coordinates)? What is most general definition of basevectors? I tought it would...

Homework Statement Consider the following ket: |ψi> = c1|e1> + c2|e2>, where ci are some complex coefficients. Find the column-vector representation of |ψi> in the |ei> basis. Find the row-vector representation of <ψ| in the <ei| basis. Homework Equations |ψi> = c1|e1> + c2|e2> The Attempt at...

'The MCSs of many vectors such as the pUC series are flanked by sequences complementary to a universal series of primers, the M13 forward and reverse primers. These priming sites are oriented such that extension of the primers annealed to these sites allows sequencing of both ends of an insert...

Homework Statement Homework Equations The Attempt at a Solution I used Pythagorean theorem to find the length of the ramp (25^2+18^2 = √949) and found the angle of elevation using tangent (Tanθ=18/25) but then got stuck on what formula to use.

I wrote the equations of the Nabla, the divergence, the curl, and the Laplacian operators in cylindrical coordinates ##(ρ,φ,z)##. I was wondering how to define the direction of the unit vector ##\hat{φ}##. Can we obtain ##\hat{φ}## by evaluating the cross-product of ##\hat{ρ}## and ##\hat{z}##...

Homework Statement Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...

Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? Homework EquationsThe Attempt at a Solution I tried using the dot product and solving for the angle but i...

What's the difference between saying that a vector's direction is north of east and north east?

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you don't see image here is the matrix which is 2X2 in MATLAB code: [9/25 12/25; 12/25 16/25] Homework...

Homework Statement x = <0, 10, 0> v1 = <4, 3, 0> v2 = <0, 0, 1> Project x onto plane spanned by v1 and v2 Homework Equations Projection equation The Attempt at a Solution I took the cross product k = v1xv2 = <3, -4, 0> I projected x onto v1xv2 [(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p I finished...