Dot Definition and 552 Threads

Homework Statement Basically, I'm looking at the property that says if the magnitude of a vector valued function is constant, then the vector function dotted with it's derivative will be zero. But I'm stuck towards the end because the proof I found online seems to skip a step that I'm not...

Hi there, I understand that taking the dot product of two four vectors automatically applies the metric tensor to the second vector. Is there a way to take write the dot product, using vector notation, in a way which keeps the signs of all of the components positive? Thanks in advance.

Homework Statement I'm doing a question that requires me to take the dot product of 2 vectors in spherical coordinates. Both vectors have only an r component, can I just multiply the r components? Homework EquationsThe Attempt at a Solution

Homework Statement at what initial speed would a projectile have to start at when ejected at 35 degrees to the horizontal from a point A to a point B which is 9.4km distance away in the horizontal and 3.3km below it. taking g as 10m/s[/B]Homework Equations I'm not really sure if these equations...

Homework Statement Maybe I missed it, but in my notes and also in documents like (http://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013/lecture-notes/MIT8_05F13_Chap_09.pdf) (equation 1.64), I see $$ \vec{r}\cdot\vec{p} = -i\hbar r \frac{\partial}{\partial r} $$ Where ##r## is...

This may seem a bit pedantic but I'm writing a report and have radicals in it and notice that some papers put the dot in different places, so my question is does it matter where you put the dot? thanks for any advice

Homework Statement Under what conditions is \left\langle{{\mathbf{x} \cdot \mathbf{p}}}\right\rangle a constant. A proof of the quantum virial theorem starts with the computation of the commutator of \left[{\mathbf{x} \cdot \mathbf{p}},{H}\right] . Using that one can show for Heisenberg...

Homework Statement Bead B has negligible weight and slides without friction on rigid fixed bar AC. An elastic cord BD has spring constant k = 3 N∕mm and 20 mm unstretched length, and bead B has a force of magnitude P in direction BC. If bead B is positioned halfway between points A and C...

Why does the Earth appear blue (mostly) when observed from outside. Blue light is more energetic than red and lower wavelength. Processes which happen on Earth seem to suggest that higher energy light arriving should be absorbed in one way or another and eventually some of it radiated away in...

Homework Statement The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...

Homework Statement [/B] Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units. a) find A dot B b) find A x B c)...

Homework Statement The Vector a= -2i -3j and is orthogonal to vector b that has the same length as a. The third vector c has the dot products ca= 8m^2 and cb= 9m^2. What are the components of c? c = ______i + _____ j m Homework EquationsThe Attempt at a Solution I know that (a⃗ +b⃗ )⋅c⃗ =a⃗...

Homework Statement https://www.dropbox.com/s/8l90hahznjlv9d0/vector%20problem.png?dl=0 Homework Equations Dot and Cross product The Attempt at a Solution although I know the dot and cross product, I'm not sure what I'm being asked or how to proceed? any help?[/B]

Hi all. I'm struggling with taking dot products between vectors in spherical coordinates. I just cannot figure out how to take the dot product between two arbitrary spherical-coordinate vectors ##\bf{v_1}## centered in ##(r_1,\theta_1,\phi_1)## and ##\bf{v_2}## centered in...

I'm currently writing my EP on various physical equations including Maxwell's equations, and I had to justify using the dot product of the normal unit vector and the electric field in the integral version. However, I can't think of a reason for not using trigonometry as opposed to the...

This is the gravitational potential energy formula $$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$ If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1 But after multiplication there is a negative sign here: "-GMm" $$U =...

Can anyone tell me why?

In a book I was reading, it says F=mv'=P' so dot producting on both sides with v F ⋅ v = mv ⋅ dv/dt = 1/2 m d(v2)/dt = d(1/2 m v^2)/dtI really don't get how v ⋅ dv/dt = 1/2 d(v2)/dt. I have seen few threads and they say it's about product rule, but they don't really explain in detail. Could...

Hi, I have following problem of double dot product (\vec a \cdot \vec b)(\vec a^* \cdot \vec c), and I have expected rusult |a|^2(\vec b \cdot \vec c), but I don't know if it is the exactly result (I am unable to find any appropriate identity or proove it), or it is just an approximation...

Homework Statement A ball is tossed straight up into the air so that it moves in the vertical direction without air resistance. Is there a point where the dot product of the velocity with the acceleration is: a. Zero b. Negative c. Positive d. now assume the ball moves in a parabolic path...

I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...

Dear All, Here is one of my doubts I encountered after studying many linear algebra books and texts. The Euclidean space is defined by introducing the so-called "standard" dot (or inner product) product in the form: (\boldsymbol{a},\boldsymbol{b}) = \sum \limits_{i} a_i b_i With that one...

Homework Statement [/B] Use vectors and the dot product to prove that the midpoint of the hypotenuse of a right triangle is equidistant to all three vertices. Homework Equations [/B] I know the dot product is A⋅B = |A||B|cosΘ ... or ... A1B1 + A2B2 + A3B3 ... + AnBn I know the...

Hi - just working through my text (studying by correspondence) on Del operator - so Curl, div etc. Came across some identities parts of which which have me confused. what does it mean when a vector is shown as multiplying something - but without dot or cross? For example F(∇.G) or ∇(F.G) or...

Homework Statement If at some particular place and time the sun light is incident on the surface of the Earth along a direction defined by the unitary vector – vˆ , where vˆ =(4, 3, 5)/sqrt (50) and with a power density P, what is the total power captured by a solar panel of 1.4 m2 and with...

Find the basis of the subspace of R4 that consists of all vectors perpendicular to both [1, -2, 0, 3] and [0,2,1,3]. My teacher applies dot product: Let [w,x,y,z] be the vectors in the subspace. Then, w-2x+3z=0 and 2x+y+3z=0 So, she solves the system and get the following: Subspace= {...

Homework Statement So a kaon moving at some speed in the +x direction spontaneously decays into one pion and one anti-pion. The anti-pion moves away with velocity of 0.8c, and the pion moves away with velocity of 0.9c. Mass of kaon = 498 MeV/c^2 Mass of pion/anti-pion = 140 MeV/c^2...

Homework Statement How can I draw a Lewis dot structure for octathiocane (S8) which is non-cyclic, net neutral, and which does not violate the octet rule? Homework Equations None. The Attempt at a Solution First, I tried drawing a straight chain molecule, but the two terminal...

I'm just trying to understand from a linear algebra standpoint how they define dot product from the inner product and how this gives rise to a definition of length and angle. somehow there is a way to combine points in space to a scalar value that unambiguously determines length and angle? Is...

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...

So, is there anyway to make the dot product change linearly? What I mean by this is when the angle is 45 degrees, I want it to be 0.5 instead of 0.7071 as you can see in this image: Instead I want 45 degrees to be 0.5, 60 degrees to be 0.33 and 30 degrees to be 0.66. Same would apply for...

I'm reading through Douglas Gregory's Classical Mechanics, and at the start of chapter 6 he says that m \vec{v} \cdot \frac{d\vec{v}}{dt} = \frac{d}{dt}\left(\frac12 m \vec{v} \cdot \vec{v}\right), but I'm not sure how to get the right hand side from the left hand side. If someone could point...

Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...

Hi everyone, I have to find out how to do cross and dot product for two vectors in non-orthogonal coordinate system. thanks

Homework Statement I've been told that the operator ##\hat n \cdot \hat {\vec L}## has the same eigenvalues as ##L_z##. Later I've been told that it has the same eigenvalues as any component of ##\hat {\vec L}##. But I am a bit confused, as far as I understand the eigenvalues of ##L_x##...

Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...

If a system is made up by two subsystems, for example, the atom and the photon. and let's assume the state of the atoms is described by |\phi\rangle, while the state of the photons can be described by |n\rangle, The Kronecker product of the |\phi\rangle and |n\rangle can be used to describe the...

I know intuitively that the Cross Product of two vectors ##\vec{A}## and ##\vec{B}## represents another vector ##\vec{A \times B}## perpendicular to it. In study of physics we come across this situation a lot. Hence I can visualize some applications of it I know that the dot product of...

So 3 days ago I had a chemistry test and part of the test included Lewis dot structures. I counted my valance electrons and distributed them equally but I have no Idea why I got these wrong.The second one I know why I got wrong but the rest of them look fine to me. I would really appreciate it...

Homework Statement I am trying to calculate the flux for the octant of a sphere, and I am trying to figure out how the mathematics, dot products, and dA works in the integral. I already did the quadrant for \hat{θ} where θ= π/2 (the bottom quadrant) and I did the left quadrant where \hat{n}...

Vectors -- dot product and cross product? Hello may i know when to dot product and cross product?? both look to same to me..

Let's say A and B are 2 vectors with length in cm and the angle between them is 170°. Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?

I am trying to understand the difference from a physical phenomena point of view, not just math. Surprisingly I think I got the cross product like in rotational momentum. You have the momentum vector and we have effective distance from the momentum vector R that needs to be perpendicular to the...

Hey everyone, This has been bugging me for a bit. I think I'm probably missing something pretty easy. A dot B= ABcos(θ), where θ is the angle between A and B. There is the little shortcut that says where B is the derivative of A, A dot B= AB. Clearly then cos(θ) = 1, and the angle between a...

As you can see, octet rule isn't satisfied for the central atom Xe, it has 2 more electrons attached to it. So does it mean, that you should first try to make sure octet rule works for any "side" atoms, and then you just put any remaining electrons to a central atom? (or central atoms?) And if...

"Projection Using Dot Product" "Finding a Force" (Boat Problem) Homework Statement ------------------------------------------------------------------------------------------- A 600 pound boat sits on a ramp inclined at 30 degrees. What force is required to keep the boat from rolling down...

I'm not sure which section is best to post this question in. I was wondering if the expression (u $ ∇) is the same as (∇ $ u). Here $ represents the dot product (I couldn't find this symbol. ∇=del, the vector differentiation operator and u is the velocity vector or any other vector

Homework Statement The value of 3i(dot)(jxk) Homework Equations The Attempt at a Solution I know the answer is 3, but could someone please explain how to work this problem?

Problem 1: Let S1 be a sphere centered at(0, 1, -3) with radius 1 and let S2 be a sphere centered at (3, 5, -9) with radius 2. Find the distance between the two spheres. problem 2: Given three non-zero vectors v1, v2, v3 we say that they are mutually orthogonal when v1 dot v2= 0, v1 dot v3=0 ...

Homework Statement The dot product of.two vectors is -1which of the following statements is true A. They must be unit vectors pointing in opposite directions. B. They must be unit vectors pointing j. The same direction. C. They must be more than 90( and less than 270 )degrees from each...