Dot Definition and 564 Threads

Hi, Im having trouble understanding something in one of my Dynamics lectures. The lecturer said that: dr/dt dotted with d2r/dt2 (where r is a vector) equals: (1/2)(d/dt(dr/dt dotted with dr/dt))... I just can't get this result. I know it has something to do with the product rule...

Homework Statement can you divide 2 vectors which are in fractions? Homework Equations example a . a / b . a (dot products) The Attempt at a Solution would it become a / b?

Homework Statement A = 2i + 3j E = 4i determine the integral of E dot dA Homework Equations Integral calculus, vectorsThe Attempt at a Solution I don't understand why one could do this. The integral is of E and dA, not E and A. How can I use A to determine dA? Do I take its derivative? Then I...

Question Let vectors \vec{A} =(2,1,-4), \vec{B}=(-3,0,1), \vec{C}=(-1,-1,2). What is the angle (in radians) \theta_{AB} between \vec{A} and \vec{B}?Important equations \vec{A} \cdot \vec{B} = \vert \vec{A} \vert \,\vert \vec{B}\vert \cos(\theta), where \theta is the angle between \vec{A} and...

Describe the surface defined by the equation: (a) \vec{r}\cdot \hat{x}= 2, where \vec{r}=x\hat{x}+y\hat{y}+z\hat{z}; (b) \left \| \vec{r} \times \hat{x}\right \|=2 For the first one, I know that is interpreted as the projection of the r vector onto the x-axis is equal to two...

Greetings. I was thinking about finding the angle between two functions, so I thought it may be elegant to turn them into vector valued functions, and find the dot product at a given variable value where the vectors lie on the same plane and are functions of the same variable. I'm going to go...

Homework Statement I need to find the momentum space function for the ground state of hydrogen (l=m=0, Z=n=1) Homework Equations \phi(\vec{p}) = \frac{1}{(2\pi\hbar)^{3/2}}\int e^{-i(\vec{p}\cdot\vec{r})/\hbar}\psi(\vec{r})d^3\vec{r}...

Homework Statement I need to determine the average speed of a dot on a spinning motor and also the time it takes for teh dot to make on revolution. Using a strobe light I determined I needed to do 3959.2 flashes/min in order to make the dot stay in place. The dot is 6.9 cm away from the center...

Homework Statement Which of the following can be computed? 1. A dot B dot C 2. A dot ( B dot C ) 3. A dot ( B + C ) 4. 3 dot A Homework Equations The Attempt at a Solution I believe that 2 and 3 are the only two that can be computed. Can anyone confirm this? Thanks.

The following notation is from the book "Frames and Bases." Let f and g be vectors in R^{n} with the usual dot product <,>. Then, what does the notation \left|\left\langle f,g\right\rangle\right|^{2} mean? Specifically, does it mean \left|\sum^{n}_{i=1}f_{i} g_{i}\right| or does it...

Hi, I'm very ashamed about getting a fully understanding of these vector product concepts. But i did a lot of search and get an idea about them. I read Feynman's lecture on physics and almost completely understand the mathematics behind their properties. In that book feynman proves that cross...

Hi! I am trying to find out where: cos\theta=\frac{a \cdot b}{|a||b|} came from. Here is mine geometrical interpretation of scalar projection: Now, (pr means projection) pr_{\overrightarrow{A}} \overrightarrow{B} = p\overrightarrow{B_0} and...

Hi All, I'm currently studying vector projections and the vector dot product. I ran into a problem on the homework I wasn't quite sure how to tackle... Any suggestions?The problem is stated as follows: Determine ||v+w|| if v and w are unit vectors separated by an angle of \frac{\pi}{6}...

Another way of stating it is the sum of the dot products of vectors B and vectors A = 0 Is this because the dot product of two vectors is 0 if they are 90 degrees to each other. So this is just adding up a certain amount of these two vector systems, and since magnetism is always normal to...

So given the common explanation here for Del dot B equals 0 to be "There are no magnetic monopoles.", since the title indicates that the equations in a vacuum have the same form, would the meaning of Del dot E = 0 mean that "There are no ELECTRIC monopoles?"...which we assume to be false...

Statement: I was wondering if the following are identical, \nabla \bullet \nabla \times \vec{A} = \nabla \bullet (\nabla \times \vec{A}) ? (#1) Also, more importantly I was wondering if someone could explain to me why the following is zero for any vector, \nabla \bullet \nabla \times \vec{A} =...

nabla dot B =0 ?? I've read the physical explanation for this eq is that magnetic monopoles do not exist. A poor explanation in my opinion. :) So, I would like it explained along these lines. (Obviously I don't unuderstand this but am giving an example of how I would like it explained)...

Homework Statement Shown are a mast and a portion of the rigging of a schooner. Members CD and EF lie in the same plane, and CD is of length 7.5 m and forms an angle of 45° with a vertical line drawn through C. Knowing that when \theta = 45° the tension in rope BD is 250N, determine, (a) the...

Homework Statement Vector A and four other vectors that have the same magnitude but differ in orientation. a) Which of those other four vectors have the same dot product with A? b) Which have a negative dot product with A? http://img195.imageshack.us/img195/7079/40191924.th.jpg (Those...

Homework Statement This is from Larson's Calculus Early Transcendentals 4th Ed (Pg. 786) A 600-pound boat sits on a ramp imclined at 30 degrees, as shown in Figure 11.32. What force is required to keep the boat from rolling down the ramp? Homework Equations The solution gives the...

Homework Statement We are studying Electromagnetic Induction right now. I understand the concepts, Faraday's Law and magnetic flux. But I don't understand what my book is doing. Homework Equations Magnetic Flux \phi=\intB∙dA Faraday's Law Emf = - d\phi/dt Emf=Electromotive force \phi=Magnetic...

Homework Statement (a) Using the dot product, show that for x, y ∈ Rn, the formula 2||x||^2 + 2||y||^2 = ||x + y||^ 2 + ||x − y||^2 holds. (b) The norm on Rn can be defined in terms of the dot product by the formula ||x|| = √(x • x). Show that the reverse is true. That is, find a...

How can I show that the binormal vector is orthogonal to the tangent and normal vector. I know i should use the dot product to determine this, however i do i actually go about doing it?

Homework Statement P = pi Evaluate \int F \cdotdr where c is the curve given by r(t) = (t+sin\pit)i + (2tcos\pit)j F = (4x3y2 - 2xy3) i + (2x4y - 3x2y2 + 4y3)j Homework Equations The Attempt at a Solution When I dot them I get an extremely long expression. \int...

Homework Statement 1. (a) Define carefully the dot and vector products of two vectors a and b. (b) Show, using the dot product, that if c - d and c + d are perpendicular then |c| = |d|. (c) The vectors a = i+2j and b = i - 2j + k form two sides of a triangle. Use vector methods to find...

Homework Statement If theta is the angle between two non-zero vectors A and B, then which of the following angles theta results in A dot B = |A x B|? Homework Equations A dot B = ABcos(theta) A x B = ABsin(theta) The Attempt at a Solution There were two choices in the multiple choice answers...

In some text, I read something like this \vec{S}_i\cdot\vec{S}_j where \vec{S}_i and \vec{S}_j are "vectors" with each components be the pauli matrices S_x, S_y, S_z individularly. My question is: if all components of this kind of vector are a 3x3 matrix, so how do you carry out the dot...

Hi, it's not quite a homework question, altought this question came up to mind when i was trying to solve a homework problem. sorry if this shouldn't be here... The thing is this, what are the conditions i should impose to f: R^n -> R in order to be able to find a g, such that [divergence of g...

In reading a book on astrodynamics I came across the following statement: \vec{a}\cdot \vec{\dot{a}}=a \dot{a} Where the dotting is the time derivative notation. I put a picture of the original text up, and it's the statement right in the middle...

I have a pretty general question about vectors. The scalar product of two vectors is a calculation of what exactly? For example, if the units of two vectors are meters, the resultant dot product would be a meters squared. So if it's a measurement of area, what area exactly? I'm very...

Homework Statement Tangent plane goes through point P=(a,b,f(a,b)). Any point on the plane is then Q=(x,y,z)=(x,y,f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)) (fx and fy are partial derivatives) and the vector \overline{PQ} is on tangent plane. Calculate dot product n.\overline{PQ} and show...

By evaluating their dot product, find the values of the scalar s for which the two vectors b=\hat{x}+s\hat{y} and c=\hat{x}-s\hat{y} are orthogonal. I understand that for the two vecotrs to be perpindicular their dot product must be 0. however I am confused how to go about this problem...

Is the result of a dot product of two vectors valid if the frame of reference unit vectors are not orthgonal? i.e. 2D 3 axis co-ordinate system as commonly used in power systems where the axis are 120 degrees apart in 2D space?

If there are three nonzero vectors.. Do you think cosine effects this example:show the three vectors must lie in the same plane? ------------- * -->dot product X -->cross product -------------- A*(BXC)=0 so we can change as.. |A||B||C|sin\alphacos\beta=0 then... we can meet...

Homework Statement I have a problem for Work which looks like this: W=[(5.0i+2.0j)]N * [(2.0i+3.0j)]m =5.0i+2.0i+5.0i*3.0j+2.0j*2.0i+2.0j*3.0j Nm =[10+0+0+6]Nm = 16 How does that work? I don't understand? Homework Equations The Attempt at a Solution

This ones a classic and it doesn't seem it's come up before. But draw 9 dots in 3 rows and columns that are equidistant, now join them up with not more than 4 straight lines. If you already know it be sure not to give the game away. Just a simple problem I thought might pass a few moments to...

Hello, I just have a question about dot products of different coordinate systems. I was wondering if anyone can explain why unit vector z(rect.) DOT unit vector r(spherical) is equal to cos(theta). As well, I was hoping if anyone could explain z DOT (Theta) = -sin(theta)?

Homework Statement I'm really at a loss here, if anyone could help me out I'd really appreciate it. Given 'a' and 'b' unit vectors, if |a+b| = root3, determine (2a-5b)dot(b+3a)

Hello, I was trying to follow a proof that uses the dot product of two rank 2 tensors, as in A dot B. How is this dot product calculated? A is 3x3, Aij, and B is 3x3, Bij, each a rank 2 tensor. Any help is greatly appreciated. Thanks! sugarmolecule

http://img297.imageshack.us/img297/2527/physicsin9.jpg i've been working with the AxB in the first one, and found that |A||B|sin(theta) = A x B, and i thought i had found my theta to be 1 degree, but i don't believe that's right. also, when i attempted to do the dot product with the C vector...

Homework Statement Find the angles which the vector A = 3i -6j +2k makes with the coordinate axes The Attempt at a Solution Let a, b, c be the angles which A makes with the positive x,y,z axes. A• i = (A)(i)cos(a) = 7*cos(a) The Solution says: A• i = (3i - 6j + 2k)• i = 3i• i...

Homework Statement The points A and B have position vectors a = (2,2,1) and b (1,1,-4) respectively relative to an origin O. (im using column notation for shorthand) Prove that OA is perpendicular to AB Homework Equations The Attempt at a Solution To be perpendicular the...

I cannot seem to figure out how to compute this dot product?! If (\nabla\times \mathbf{v})=(4z^2-2x)\hat{i}+2z\hat{k} and d\mathbf{a}=dydz\hat{i} Then shouldn't the DOT PODUCT be: (\nabla\times \mathbf{v})\cdot d\mathbf{a}=(4z^2-2x)\hat{i}*dydz\hat{i}=(4z^2-2x)dydz ? But the book...

If you look up dot product in http://en.wikipedia.org/wiki/Dot_product" , under 'properties' it states the following: "The dot product is not associative, however with the help of the matrix-multiplication one can derive: \left(\vec{a} \cdot \vec{b}\right) \vec{c} =...

Hi Wondering if someone could help me satisfy my curiosity. Hopefully a very simple for someone who knows. I have been given values for Voltage and Current. To calculate Q (dot), I know Q(dot)=V * A. The units for this are Watts / J/s / Nm/s.. How can Voltage multiplied by a current...

I have been searching for a way to relate known concepts (known to me) to the computation of the dot product in an effort to understand why it takes the form it does. I ran into a little snippet in a classical dynamics book that seems like it just may be the ticket. Here is what it says...

I was woundering what exactly is the dot product and by that I mean what does it represent because I know the equations but it just seems to spit out a random number. I do not get what this number is supposed to mean. I know how it is usefull to solve many different problems and I know how to...

Hello, I was messing around with subscript summation notation problems, and I ended up trying to determine a vector identity for the following expresion: \overline{\nabla}(\overline{A}\cdot\overline{B}) Here are my steps for as far as I got: \hat{e}_{i}\frac{\partial}{\partial...

Homework Statement Show using cartesian components that d/dt(a.b)=(da/dt).b+a.(da/dt) The Attempt at a Solution a= axi+ayj+azk b=bxi+byj+bzk a.b=axbx+ayby+azbz d/dt(a.b)= d/dt(axbx+ayby+azbz)

Hello, I have this problem that asks the following Homework Statement Find two vectors v1 and v2 whose sum is (-1,0) where v1 is parallel to (5,-5) while v2 is perpendicular to (5,-5). Could someone "walk" me thought the steps to find v1 and v2... I'm confident I can make the...