Dot Definition and 564 Threads

Homework Statement In R^2, vectors x = (x1, x2) and a = (a1, a2). For fixed a, det(a, x) is a scalar-valued linear function of the vector x. Thus it can be written as the dot product of x with some fixed vector w. Explain why w is perpendicular to a. Do not use an expression of w in terms of...

I know how I would be able to do this using projection, but am not so sure with dot products. Do I dot the normal vector with an imaginary point and then figure something out from there? If the normal is a= <a1,a2,a3> and the random point is (p1,p2,p3) If I dot them, I would get a1p1 +...

Let A ,B and C represent vectors. we have 1) d/dt (A . B) = A. dB/dt + dA/dt .B 2) d/dt [ A . (BxC) ] = A . (Bx dC/dt) + A . ( dB/dt x C) + dA/dt . (B xC) now the problem in these formulas is that we know that Dot product between two vectors and Scalar triple product of vectors is...

Vector A and vector B are expressed in component form. A = [2.32,-5.16,7.88] B = [-1.12,3.45,-12.8] The standard arrow representation of these vectors and that of can be arranged to form a triangle in a plane that represents the geometric equivalent of the subtraction operation. The...

say for example for 2 vectors A.B=0 and for another pair A.C=0.is it necessary that B is parallel to C.If yes how?

I have performed numerous calculations of dot products throughout my math courses, but I think I lack a fundamental understanding of what it actually means, beyond the abstract way I have been taught to deal with them. I know the definitions (it's the inner product, or the projection of A on to...

If I take the Dot Product of two vectors, say A and B, I get: AxBx + AyBy + AzBz And then when I add those terms, I get the magnitude, right? So when one of those terms are negative, that means I could end up with a negative magnitude? I thought magnitude had to be positive.

How, precisely, do you get/derive the Bcosθ term? Is it simply [Cosθ=A/B] --> [BCosθ = A] ? It can't be that simple because then how is the extra length of vector A fit into [*A*Bcosθ]? I feel pretty confused as to what is going on here. To summerize, A x B = [ABcosθ] makes little...

I started to read Analytical Mechanics. It said that if holonomic constraints are defined as: r = r(q1, q2, ... qn, t) (or without time) This equation holds (dot cancellation): ∂r'/∂q_k' = ∂r/∂q_k where ' specified derivatives. And the question was given to check if it works for...

Homework Statement Please check attachment or picture below. http://i.imgur.com/PIwt0.png Homework Equations The Attempt at a Solution Since there is no enclosed current for path AB, shouldn't it just be 0? Thanks!

So my book says Lets suppose, We have two vector v and u w=projection of u ev= unit vector θ=angle between the two w=(u.ev)ev or w=( (u.v)/(v.v) )v Now, the second equation is fairly easy to understand if we understand the first one because ev= v / |v| What is...

The problem: Solution in the spoiler: I don't know how to do the problem (a), but I also don't understand the answer (top of coil 3?). Can you give me the process on how to do the problem (a), i.e. in general how do I assign dots to coils in circuits? :)

Hello, I am trying to find the angle between two unit vectors but I was wondering what I am supposed to do when the dot product is greater than 1 or less than -1. For example -0.0288067i + -0.989524j + -0.141463k 0.169194i + -0.0644865j + -0.983471k

Homework Statement Assuming that ∅ is a differentiable scalar valued function and F a differentiable vector field, derive the following identities. a)∇(dotted with)(∅F) = ∇∅(dotted with)F + ∅∇(dotted with)F b)∇(crossed with)(∅F) = ∇∅(crossed with)F + ∅∇(crossed with)F Homework Equations The...

whats the difference between simple product and dot product?

Dot product proof question? Hi, I'm having trouble understanding the proof of the dot product in three dimensions (not using the cosine rule approach). Here's what I have for the 2D proof: u = u1 i + u2 j v = v1 i + v2 j u.v = u1v1 + u2v2 u.v = |u| |v| cos(θ) => u1v1 + u2v2 = |u| |v|...

Given the following cross product equation: \vec{A}\times\vec{B}=\vec{C} How to express \vec{A} in term of \vec{B} and \vec{C} (or \vec{B} in term of \vec{A} and \vec{C} ). I think the question I want to ask can also be rephrased as if one was told that a known vector when cross product with...

Homework Statement A cutting tool under microprocessor control has several forces acting on it. One force is \vec{F}=-αxy2\hat{j}, a force in the negative y-direction whose magnitude depends on the position of the tool. The constant is α=2.50 N/m3. Consider the displacement of the tool from...

Homework Statement I have to draw Lewis structures and Lewis dot structures of these salts The Attempt at a Solution I attached images of how I tried to traw Fe(ClO4)3 and (NH4)2SO3 but I can't figure anything out about Al2(SO4)3

I have a question regarding cross products and dot products. What is the difference, and are there any similarities? What ARE cross products and what are their functions? What ARE dot products and what are their functions? What do we use them for? Thank you, Joyci116

This is from my homework, I was moving along nicely until I hit this problem, (there's another just like it right after this). I can't find reference for solving this in the chapter I am looking at. The answer is in the back of the book….-2911. Can someone explain this to me? ||\mathbf{u}|| =...

Homework Statement What is the dot product of two unit vectors in spherical coordinates?Homework Equations A∙B = ||A|| ||B|| cos(\theta) = cos(\theta)The Attempt at a Solution The above equation is the only relevant form of the dot product in terms of the angle \theta that I can find. However...

I am searching for physical realizations of universal logic operations (phase rotation, CNOT, Hadamard) in single-dot excitionic qubits. Phase rotations are easy to implement with sinusoidal electric fields but my literature search for CNOT and Hadamard gates runs dry. I can find them in spin...

Hello. :smile: I understand most of the work involved with these types of questions, but there is one point in an example I'm following that I don't understand. Homework Statement Evaluate: I = \int{(z^2)}dS over the positive quadrant of a sphere, where (x,y > 0). Homework...

[b]1. For two differentiable vector functions E and H, prove that (Delta (dot) (e X h) = H (dot) (delta X e) - e (dot) (Delta X h) [b]2. Cross product and dot product. The Attempt at a Solution First I took did the left side of the equation, I took the cross product of vectors e and...

Homework Statement In real-number multiplication, if uv1 = uv2 and u ≠ 0, then we can cancel the u and conclude that v1 = v2. Does the same rule hold for the dot product: If u • v1 = u • v2 and u ≠ 0, can you conclude that v1 = v2? Give reasons for your answer. Homework Equations...

dl (dot) r hat in computing potential?? when computing the line integral "from infinity" back toward charge, the direction is pointing to the circle. But r hat is pointing away from circle. So vector dl should equal magnitude dl times negative r hat, which would change sign of potential...?

Homework Statement obtain the dot product of the two vectors F= 10i + 6j - 3k lb and B= 6i -2j ft Homework Equations F dot B = FxBx + FyBy + FzBz x is for the x components y is for the y components z is for the z components The Attempt at a Solution F dot B = (60 + -12 + 0) I ended...

Hi, here's the problem: for m = {{a, b}, {c, d}}, m \cdot m is suppose to = {{a^2 + b c, a b + b d}, {a c + c d, b c + d^2}} It's been ages since I took linear algebra and now can't figure out how this works. Thanks for your help!

i know that del.v=divergence of vector v and del x v=curl of vector v can anyone justify for the same? how dot product is physically connected to divergence property?

Homework Statement This is from Peskin & Schroeder p. 14 in case anybody's interested. The function is U(t)=\frac{1}{(2\pi)^3}\int d^3p\, e^{-it \sqrt{p^2+m^2}}e^{i\vec p\cdot(\vec x-\vec x_0)} Homework Equations The Attempt at a Solution Essentially you write out the dot product as p\cdot...

vectors a - b + c = 0 ,determine the values of a dot b - adot c - b dot c if |a|=1, |b|=2 and |c|=3

I'm learning about dot products, and I'm having a bit of trouble grasping why axbx + ayby + azbz = ab*cosΘ. I understand how it works in two dimensions, I think, but three is still fuzzy. This is what I came up with for two dimensions. The angle between the vectors is simply the difference...

How can I make something like dot products tangible? Are there real life examples where dot products are used? This is for motivating students. Aware that we can test for orthogonality. Thanks in advance for any replies. Really appreciate anyone taking time out to answer these questions.

So I am doing my lewis dot diagram work, does it matter where i put the valence electors? for example oxygen has 6 valence electrons, i go with using the N E S W (North, east south, west) I put 2 north, 2 east, 2 south but none of west(6 in total so far) but the book puts them in the...

Homework Statement Given A . B=0 and A x C=0...whats the angle b/w B and C? Homework Equations The Attempt at a Solution..

\vec r = \hat x x + \hat y y + \hat z z \;\Rightarrow \;r = \sqrt { x^2+y^2+z^2} \;,\, \hat r= \frac { \hat x x + \hat y y + \hat z z}{ r} I want to find the dot product (\hat x -\hat r \frac x r) \cdot (\hat x -\hat r \frac x r) 1) \hat x -\hat r \frac x r = \hat x - \frac { (\hat x x...

Homework Statement A coil with N loops and radius R is surrounds a very long solenoid of radius r and n turns per meter. The current in the solenoid is varying sinusoidally with time according to the relation I(t)=I0sin(2πft) where I0 is the maximum value of the current, and f is its...

Hello Forum, I understand that a quantum dot is a 3 dimensional confinement of an electron inside which the electron can only have quantized energy (quantized energy levels)...a quantum wire is a 2D trap, a well a 3D trap... What is so special about confining electrons in space? Why so many...

I thought the dot product was commutative but there must be something about it that I don't understand. Perhaps the dot product is commutative only for vectors and not for tensors generally? In Kusse and Westwig, p70, it says that the order of terms matters because, in general, \hat{e}_j...

Hi all! Can anyone tell me What this picture of a quantum dot means?? The signifigance of what this exact picture stands for. What does it prove??

Homework Statement A force F=3i ̂+0.5j ̂-5k ̂(N)is applied to a partial located at r=2i ̂+4k ̂(m) Determine the torque vector? Homework Equations The Attempt at a Solution

Homework Statement As illustrated, a ball of mass m_1=0.25 kg and velocity V_(0_1=+5.00 m/s) collides head on with a ball of mass m_2=0.8 kg that is initially at rest. No external forces act on the balls. If the collision is elastic, what are the velocities of the balls after they collide...

Hi again, I don't want it to seem like I'm spamming topics here, but I was hoping I could get help with this dillema, too. So, let's say that, in affine 2-dimensional space, we have some two, non-orthogonal, independent vectors, and we also pick some point for an origin O. This clearly...

Let \vec w(t) \;,\; \vec v (t) be 3 space vectors that is a function of time t. I want to verify that: \frac {d(\vec w \cdot \vec v)}{dt} = \vec v \cdot \frac { d\vec w}{dt} \;+\; \vec w \cdot \frac { d\vec v}{dt} I work through the verification by splitting w and v into x, y, z...

Seen over downtown Toronto at 12:45. Dot matrix skywriting. Cool. At first I thought it was one plane with a series of pods dragging below it, but we were able to actually spot five planes flying in formation. The letters are so perfect that the 'puffing' is obviously centrally...

Homework Statement Note: \nu is del could not find it... I need to prove the \nu*E=0 and \nu x E=-dB/dtHomework Equations E(s\phizt)=(Acos(Kz=wt)/s)s^ The Attempt at a Solution so for the first one \nu*E=0 I thought it would be d/ds(E) but what they did was 1/s d/ds(s E) no idea why they...

Homework Statement i dot 1/√2( i + j) Homework Equations The Attempt at a Solution I think that perpendicular vectors are zero are dotted together, and parallel vectors dotted are 1. I am tempted do do the distributive property where i dot i is 1 and i dot j is zero, but I...

Homework Statement \vec r = <x, y, z>, r = \left | \vec r \right | The problem is, verify the identity: \nabla \cdot (r\vec r) = 4r Homework Equations My book has the following property: (c\vec a)\cdot \vec b = c(\vec a \cdot \vec b) The Attempt at a Solution I tried using...

Homework Statement What is the electric potential at the point indicated with the dot in the figure? http://img842.imageshack.us/i/29ex26.jpg/ Homework Equations E = V_c / d ? V = E*s? V = k * q / r ? The Attempt at a Solution I'm really rather confused by this problem...