Dot Definition and 564 Threads

Homework Statement let u be a nonzero vector in space and let v and w be any two vectors in space. if u.v = u.w and u x v = u x w, can you conclude that v=w? give reason for your answer. Homework Equations The Attempt at a Solution v is not necessary equal to w since u is nonzero...

pretty much this is all i was given. I have no idea how to even approach it. I do not need an answer (would be nice though), just an idea on how to go about starting it.

Homework Statement See the image http://tinypic.com/r/33z6vz5/7 Homework Equations The rules of dot product multiplication. The Attempt at a Solution I've determined that 2 of the solutions are valid, while two of the choices are invalid. I thought C and D looked correct, making A...

This is not a homework question, but a derivation in my class which I can't get around. Homework Statement Step1 F=ma Step2 \vec{F} = m\frac{d\vec{v}}{dt} Step3: Multiply both side by v \vec{F}.\vec{v} = m\vec{v}.\frac{d\vec{v}}{dt} Step4 Power = \frac{d}{dt}\frac{1}{2}m\vec{v}.\vec{v}...

Homework Statement Under what conditions are the following true? a) |\mathbf{a}\cdot \mathbf{b}| =|\mathbf{a}||\mathbf{b}| b) (\mathbf{a} + \mathbf{b}) \cdot (\mathbf{a} - \mathbf{b}) = |\mathbf{a}|^2 - |\mathbf{b}|^2 Homework Equations None. The Attempt at a Solution a) I...

Homework Statement Let A(theta)x = b for each theta in S. Calculate, (x dot b)/(|x||b|) A = [cos(theta) -sin(theta) sin(theta) cos(theta)] How is this related to theta? Recall that x dot y and |x| are the standard dot-product and magnitude, respectively, from vector-calculus...

Hello, I have a doubt regarding dot convention in magnetically coupled circuits. In book A, the following is stated: But in book B, this is stated: In book B, why the inducted voltage of the second mesh (-j w M I1) has that negative sign ? According to dot convention, it is supposed that...

please prove : nabla(a dot b)=(b dot nabla)a+(a dot nabla)b+b cross nabla cross a+a cross nabla cross b; (a and b are all vectors) when I was proving it,I found it impossible to go from right side to left side. I don't know whether '(b dot nabla)a = b (nabla a)' is right or not , when...

hi, I'm trying to follow a derivation in a paper and this equation is confusing me: (u'.\nabla)U = (\nablaU).u' Where U and u' are velocities. The operation of del on the vector U without a dot or cross product is giving me some grief. Can someone explain how this works to me...

A person pulls a wagon up an incline that makes an angled of 30 deg with the horizontal with a force on the handle of 30 pounds which makes an angel of 30 deg with the incline find the work done in pulling the wagon 100 ft 20cos30 will be a force along the surface of the incline and since...

if A = 2i^+6k^ B=6i^+5j^ find A.B if A.B=0 then what do u conclude from it? one more question if A = 6i^+9k^ and B=-4i^+4j then find A+B,A-B,A.B

S(\vec{q})= \int_0^r exp(i\vec{q}\cdot\vec{x})4\pi x^2 \ dx How would one approach this integral? I tried to "ignore" the dot product and proceeded with exp(i\vec{q}\cdot \vec{x})=exp(iqx) and got a wrong answer.

Homework Statement n. Let r1 and r2 be differentiable 3-space vector-valued functions. Directly from the definition of dot product, and the definition of derivative of vector- valued functions in terms of components, prove that d/dt (r1(t) • r2(t)) = r′1(t) • r2(t) + r1(t) • r′2(t). Homework...

I have tried looking this up on the net without success. This is a (I think) classic psychology experiment in which subjects are asked to describe the movement of a small black stationary dot painted on a white wall. Some perceive the dot as stationary and others perceive that the dot moves...

i have started to use dot convention for magnetically circuit. my understanding is that if the currents for primary winding and current in the secondary winding are clockwise and the dots are ontop of the inductors then the mutual inductance value would be negative because the secondary winding...

Homework Statement 1. Evaluate \int_{S}\int curl F \cdot N dS where S is the closed surface of the solid bounded by the graphs of x = 4, z = 9 - y^2, and the coordinate planes. F(x,y,z) = (4xy + z^2)i + (2x^2 + 6y)j + 2xzk 2. Use Stokes's Theorem to evaluate \int_{C}F\cdot T dS...

If X is an N vector, is it 1) possible for X*X to be negative? 2) if x*x=0, what is X. I am having trouble writing the proper proof. for 1 I stated that it is impossible for X*X to be negative bc if x is positive, X*X is positive and if x is negative, -X*-X is still positive. for 2 I...

hi, i don't really understand what's the difference between vector product and dot product in matrix form. for example (1 2) X (1 2) (3 4) (3 4) = ? so when i take rows multiply by columns, to get a 2x2 matrix, i am doing vector product? so what then is dot producT? lastly...

i'm reviewing for a test and I can't remember how to do the cross product of (2A)x(3B) or how to find the angle theta when given components. or dot product: 2A . 3B

Homework Statement Given triangle ABC with vertices A(4, 1, 7), B(-2, 1, 1) and C(-3, 5, -6)..is ABC a Right triangle Homework Equations The Attempt at a Solution I took the dot product of vertices A(4, 1, 7).B(-2, 1, 1), and it gives 0..but however I am a little confused, as...

Homework Statement Expand and simplify: (2\vec{a} + 3\vec{b}) .(5\vec{a} - \vec{b} Homework Equations The Attempt at a Solution I tried expanding it, but was a little confused, and would really appreciate any help..would it be (2\vec{a})(\vec{a}) = 2 \vec{a}2? Thanks..

Homework Statement what is the dot product of G{\bullet}A where A = \left(\frac{a_3}{l}-\frac{{a_1}}{h}\right) and G = 2{\pi}h{\frac{{a_2}}x{{a_3}}}{{a_1}{\bullet}{{a_2}}x{{a_3}}} Homework Equations The Attempt at a Solution The answer is zero and I've got the worked solution...

Homework Statement This isn't so much a problem of calculation, so much as it is I need to know if i did it right, you'll see what I mean. vectors v=(2,0,2), u=(-1,1,0), w=(0,-1,1) Computer the quantities that make sense (a period denotes the dot product, x denotes cross product)...

By evaluating the dot product, find the values of the scalar s for which the two vectors b=X+sY and c=X-sY are orthogonal also explain your answers with a sketch: my working (X,sY).(X,-sY) has to equal 0 for them to be orthogonal x.x = 1 since they are unit vectors...

Homework Statement Show that the dot product of vectors a and b is equal to 1/4|a+b|^2 - 1/4|a-b|^2 Homework Equations a dot b = |a||b|cos(theta) a dot b = a1b1 + a2b2 + ... The Attempt at a Solution I've tried using the combination of the cosine law and those two above dot...

Not so much an actual problem, more like concepts. What exactly is the dot product? How about the cross product?

I am reading through David Widder's Advanced Calculus and he abbreviates a determinant as: \left( \begin{array}{cccc} r_{1} \ s_{1} \ t_{1}\\ r_{2} \ s_{2} \ t_{2}\\ r_{3} \ s_{3} \ t_{3}\\ \end{array} \right) And refers to it by (rst). He then states...

Homework Statement My book states as follows: --- If u and v have the coordinate vectors X and Y respectively in a given orthonormal basis, and the symmetric, linear map \Gamma has the matrix A in the same basis, then \Gamma(u) and \Gamma(v) have the coordinates AX and AY, respectively. This...

OK, this has been bugging me for a while. Why is it that \mathbf{v} \cdot \frac{d \mathbf{v}}{d t} = 1/2 v^2 where regular v is just the magnitude of bold v or more specifically where does the 1/2 coefficient turn up.

In what follows, I'll use bold for 4-vectors and an arrow over a letter to denote a 3-vector. I'll use a dot both for the Minkowski dot product and the Euclidean one, and multiplication of real numbers; the meaning in each case should be clear from the symbols on either side. \vec{v} and \vec{a}...

Why not make dot(u,v)=transpose(u)v rather than transpose(v)u?

Homework Statement I have came up with an example to illustrate my question. There is a rod, which can turn around p1. p1p2 = (-1+j) m p1p3 = (-3 + 3j) m p1p4 = (1 - j ) m F1 = (1+3j) N F3 = (-1 - 2j ) N F4 = unknown, orthogonal to the rod compute F2_n, orthogonal component of F2 to the...

Homework Statement Suppose that A is an n x n matrix such that A(Transpose)A=I. Let x be any vector in R^n. Show that llAxll=llxll; that is, multiplication of x by A produces a vector Ax having the same length as x. Homework Equations Sqrt(x(transpose)x)=llxll The Attempt at a...

What is significance of the trig functions in both the cross and the dot product? I understand what the dot and cross products are, how they work, and what they give...but I don't understand why the dot product uses cosine and the cross product uses sine?

This question has a few parts. r = i + 2j + 3k s = 2i - 2j - 5k t = i - 3j - k Evaluate: a)(r.t)s - (s.t)r b)(r x s) x t. deduce that (r.t)s - (s.t)r = (r x s) x t can you prove this relative true for any three vectors a)(r.t)s - (s.t)r (r.t)s well I don't know...

Hi, Can someone tell me if: -E dotted with ( A + B ) is equal to -E.A -E.B where E, A and B are all vectors What I mean is, does the minus sign appear on the E.B bit as well? Also, is \int \frac{d}{dt} (A) dV equal to: \frac{d}{dt} \int (A) dV Thank you

A dot (representing vibration) on a slinky exhibits simple harmonic motion as the longitudinal wave passes. The wave has an amplitude of 5,4 * 10^-3 m and a frquency of 4,0 Hz. Find the maximum acceleration of the dot. Please could you explain what equations to use and how to answer in...

In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ? Cross product or dot product?

Homework Statement Let C be the triangle from (0,0,0) to (2,0,0) to (0,2,1) to (0,0,0) which lies in th plane z=y/2. If F(x,y,z)=-3y^2i+4zj+6xk, calculate integral of C F dot dr using Stoke's Theorm. Homework Equations For the curl of F, I obtained -4i-6j+6yk. For N, I obtained...

Homework Statement determine the electron dot structure of molecules a and b http://session.masteringchemistry.com/problemAsset/1144353/2/MMAt.05.067.jpgHomework Equations The Attempt at a Solution A) ::O: H | | H-C=N-HB) H | .. H-C-N=C=O:: | H I am not at all sure...

Can someone explain to me what a dot product and vector product of two vectors are? Be as detailed as possible please! And also why does the right hand rule for vectors work?

Hello all :smile:, I am interested in the following problem: In an ensemble of atoms, the forces on atom A and atom B are given by the vectors Fa=Fax+Fay+Faz and Fb=Fbx+Fby+Fbz, respectively. Their respective positions are given by, Pa=Pax+Pay+Paz and Pb=Pbx+Pby+Pbz I have two...

Hello all :smile:, I am interested in the following problem: In an ensemble of atoms, the forces on atom A and atom B are given by the vectors Fa=Fax+Fay+Faz and Fb=Fbx+Fby+Fbz, respectively. There respective positions are given by, Pa=Pax+Pay+Paz and Pb=Pbx+Pby+Pbz I have two...

Homework Statement Prove that, if \vec{r}(t) is a differentiable vector valued function, then so is ||\vec{r}(t)||, and \vec{r}(t) \bullet \vec{r'}(t) = ||\vec{r}(t)|| ||\vec{r}(t)||'Homework Equations I know how to do a dot product, but what bothers me is the fact that the question involves...

Homework Statement Let \vec{A}, \vec{B}, and \vec{C} be three vectors which are all not in the same plane. Show that \vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\vec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B}) Homework Equations Don't know :( The Attempt at...

What does the following mean - \int \textbf{F} \cdot d \textbf{r} I know that its equal to work done. but i have problem in understanding it, what's the varibale. i am familiar with integrate cosxdx. what's is similar to dx in above equation. is it ds. Now how can one get to this from above...

I’ve got a confusion. We know a 1x3 row matrix is a 3-vector i.e. x= [ a b c] Matrix x can be written in vector notation like x= a i + b j + c k where i, j, k are unit vectors along x,y & z axes. For dot product of x.x = a2 + b2 + c2 when x= a i + b j + c k But according to...

Ok I have seen the tensor double dot scalar product defined two ways and it all boils down to how the multiplication is defined. Does anyone know which is correct? I believe the first one is correct but I keep seeing the second one in various books on finite element methods. 1. \nabla \vec{u}...

In the famous photo "Pale Blue Dot" of the Earth from outside the solar system, one can see "bands" of colour around the Earth. What causes these bands? Is that an optical illusion? Does the band in which Earth is found describe the Earth's orbit? What are the other coloured bands? What gives...

I am having problems with this questions my physics teacher gave us. Since he doesn't explain things well, I do not know how he got an answer of 66. Can you please explain to me how to get this answer? THX. For the following three vectors, what is C*(A X 3B) (the "*" is suppose to be a dot)...