Scalar product Definition and 91 Threads

Homework Statement From the inequality |a.b| <= |a||b| prove the triangle inequality: |a+b| <= |a| + |b| Homework Equations a.b = |a|b| cos theta The Attempt at a Solution Making a triangle where side c = a+b. Don't know how to approach the question. Thanks.

Homework Statement If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: -the vectors must be parallel and in the same direction -the scalar product of the vectors must be negative -none of these -the scalar product of the vectors must be...

Hello! I am preparing for an exam, I didn't really had much time for, and it would be nice of you if you could help me! Homework Statement Draw a figure, so that the following is true: (AC - AB) * AB = 0 2. The attempt at a solution Since I had to miss some classes, I don't really have...

the potential difference between b and a is defined as follows: V(b) - V(a) = -∫E \bulletdl the integral is taken from a to b. so the potential of a positive charge, with infinity as reference, is V(r) - V(infinity) = V(r) = -∫E \bulletdl the integral is from infinity to r...

Homework Statement Let vectorB= 5.45 m at 60°. Let C have the same magnitude as A and a direction angle greater than that of A by 25°. Let B·A = 32.4 m2 and B·C = 35.1 m2. Find the magnitude and direction of A . Homework Equations A·B=MagAxMagBcosθ The Attempt at a Solution I just...

Homework Statement A x (B dot C) (A x B) dot C They are vectors. Homework Equations A x (B dot C) (A x B) dot C The Attempt at a Solution I know how to do my homework, but I am confused on these formulas. Is the first formula "A x (B dot C)" the same as the second one? I know the...

Homework Statement Look up, figure out, or make an intelligent guess at the product rule for the scalar product. That is, a rule of the form d/dt [a(t).b(t)] =?+? Verify your proposed rule on the functions a(t) = ti + sin(t)j + e^(t)k and b(t) = cos(t)i - t^(2)j - e^(t)k: Homework...

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...

Homework Statement I am working through Boas' Mathematical Methods in the physical sciences book and I don't understand the triple scalar product and torque example. k [dot] (r X F) = 0 0 1 = xF_y - yF_x x y z F_x F_y...

What is the general strategy in solving vector equations involving grad and the scalar product? In particular, I want to express \Lambda in terms from \mathbf U \cdot \nabla\Lambda = \Phi but it looks impossible, unless there is some vector identity I can use. Thanks in advance.

Homework Statement Is it possible to use the triple scalar product to solve anything greater than a 3x3 matrix? Homework Equations Ax + By + Cz + D = 0 The Attempt at a Solution In terms of planes, the triple scalar product can be used to determine if the NORMALS of the planes...

Homework Statement This is what we are given in the assignment: Recall a definition of scalar product on complex numbers. Let A = [[3,1],[1,2]]. Prove that the product as defined by: * => dot product u * v := uT * A * conjugate(v) ( = Sum from i,j=1 to 2; uiAijconjugate(vj) )...

I'm trying to derive the equation for the scalar product of one particle momentum eigenvectors \Psi_{p,\sigma} ( p is the momentum eigenvalue and \sigma represents all other degrees of freedom), in terms of the little group of the Lorentz group with elements W that take the standard four...

We use the antisymmetric Fock space ( "fermions"). We denote by c(h) a creator operator. I need to evaluate the following quantity: < \Omega , \big(c(h_1)+c(h_1)^{*}\big)\big(c(h_2)+c(h_2)^{*}\big) \ldots \big(c(h_n)+c(h_n)^*\big)\Omega> where \Omega is the unit vector called vaccum...

Hi all, I need to evaluate the following equation : \mathbf{n} \cdot [\mathbf{\sigma} + \mathbf{a} \nabla\mathbf{\sigma}]\cdot\mathbf{n} where \mathbf{n} is the normal vector, \mathbf{a} a vector, and \sigma the stress tensor such that : \mathbf{\sigma} \cdot \mathbf{n} =...

How do I show that the scalar product is time independent? I have: \frac{d}{dt}\int\Psi^{*}_{1}(x,t)\Psi_{2}(x,t)dx = 0 And have proceeded to take the derivatives inside the integral and using the time dependent Schrodinger eq. ending up with...

[PLAIN]http://img62.imageshack.us/img62/5319/49966749.png What is the scalar multiples of a vector actually? I was thinking L = c[2 1 2]T Then I looked for projection of v on L. But I got c in my answers which are not supposed to be...

Homework Statement Vector V_1 points along the z axis and has magnitude V_1 = 80. Vector V_2 lies in the xz plane, has magnitude V_2 = 51, and makes a -49o angle with the x-axis (points below x axis)Homework Equations A.B=ABCos(theta)=AxBx+AyBy+AzBz Cos(theta)=(AxBx+AyBy+AzBz)/AB The Attempt...

This isn't homework, but I worked this out to become more fluent with expressing these operations using sums, indices, etc. This is from my Vector Analysis course, and the professor said understanding this would make the rest of the course smooth sailing if I get all these concepts down. I'm...

How do you find the scalar product of two non-orthogonal many particle states? For example <\leftarrow,\rightarrow|\uparrow,\downarrow> I wanted to express both as a 4-vector in the up/down basis, but this seems weird, since then a state |\uparrow\downarrow+\downarrow\uparrow> is like...

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}...

Homework Statement Find the scalar product of the 2 vectors. Vector A is north of east at 70 degrees with a magnitude of 3.60m Vector B is south of west at 30 degrees with a magnitude of 2.40mHomework Equations ABcosxThe Attempt at a Solution I did dot product using the formula...

Homework Statement If a and b are 4-vectors give the definition of the scalar product a.b and demonstrate its Lorentz invariance Homework Equations The Attempt at a Solution So (with 4-vectors double underlined!) a.b = a0b0-a1b1-a2b2-a3b3 a' = (a0*gamma - beta*gamma a1 ...

http://img520.imageshack.us/img520/9580/56788025.th.jpg See the problem above. I can do all of the problem, barring the last part. I have found r and r.r: http://img520.imageshack.us/img520/1590/29349935.jpg How does this allow me to find the minimum and maximum distance...

To any teachers or students, either instructing or taking, a Calculus-based Physics I course: I tutor a calculus-based general physics course in kinematics, and similar topics, and, I recently had a student approach me about his inability to grasp the scalar/dot product, in vector operations...

Euclidean norm is defined usually as|v|2= g(v,v), where g is a nondegenerate, positive definite, symmetric bilinear form. But how can make it backwards? What properties must norm have that g(v,w) = (|v+w|2 - |v|2 - |w|2)/2 be a positive definite, symmetric bilinear form?

Homework Statement Let (u,v)1 be a second Hermitian scalar product on a vector space V. Claim: There exists a positive transformation T with respect to the given scalar product (u,v) such that (u,v)1 = (Tu,v) for all u,v in V. Homework Equations A transformation T is positive if...

Hey, in my textbook they keep doing this and I can't follow for example r.\ddot{}r = 1/2 \ddot{}r^{}^2{} and r.\dot{}r = 1/2 \dot{}r^2{}. Can anyone explain this to me? I know I should probably know it. P.S Can't quite get the dot product to look right apologies.

Is there a general way of proving that the scalar product xuxu = (x0)2 - (x1)2 - (x2)2 - (x3)2 is invariant under a Lorentz transformation that applies no matter the explicit form of the transformation.

Attached is a .jpg of my problem. I know how to find the scalar product of B*C (I think... 5, right?), but I don't really know where the 2 and 3 come into play. I've tried multiplying the values of C by 3 and then finding the scalar product, then multiplying the quantity by two, but that was...

Hello there When multiplying two vectors, why do we multiply them with the cosine of the angle between them? why not the sine of the angle? Thanks.

Homework Statement i have 3 vectors a,b,and c. on matlab, i have to find the triple scalar product: b.(c x a) Homework Equations The Attempt at a Solution i typed it in the script file as: b'*cross(c,a) but i got a 3x3 matrix...shouldn't the answer be one fixed value since...

Use the definition of scalar product, a·b = ab cos , and the fact that a·b = axbx + ayby + azbz (see Problem 46) to calculate the angle between the two vectors given by a = 2.0 i + 6.0 j + 2.0 k and b = 4.0 i + 3.0 j + 6.0 k. AdotB= 8i + 18j + 12k A=sqrt(2^2 + 6^2 + 2^2)=6.63 B=sqrt(4^2 +...

Homework Statement What surface is represented by r . a = conts. that is described if a is a vector of constant magnitude and direction from the origin and r is the position vector to the point P(x1, x2, x3) on the surface? The Attempt at a Solution I know that the dot product of two...

Hi everyone, How would I go about proving that the scalar product of two four-vectors (A,B) is invariant under a Lorentz transformation?

Homework Statement What is the value of a(dot)(a(cross)b) ? Why? I am supposed to find an actual value. Sorry I don't know code, these variables are all vectors. A is dotted with vectors a and b which are cross product. Homework Equations I know this can be written as a determinate of...

hey, ive been given a problem where vector a = 2i + 3j and vector b = \lambdai + 12j and also told that these vectors are parallel of each other. i understand since the vectors are parallel of each other, the angle between them would be equal to zero, thus i could apply the scalar product rule...

Hey, Today I was given a problem to solve in class and was told to complete it for homework. This problem is as follows: The line y=mx + c has a gradient m and cuts the y-axis at (0,c). Thus we can write the parametric vector equation of the line as: r = cj +\lambda (i + mj) Using this...

Just a few questions from this set I have to do, I missed the class on these topics so I'm just a little confused with these last few problems. http://img161.imageshack.us/img161/2307/problem43eu.png Concerning sets 38-39, and 40-41, I've grasped how to scalar multiply these vectors, but...

Consider the two vectors M =(a,b) = ai+bj and N = (c,d) = ci +dj, where a =4, b =4, c = -1, and d = 1. a and c represent the x-displacment and b and d represent the y-displacment in a Cartesian xy co-ordinate system. Note: i and j represent unit vectors(i.e. vectors of length l)in the x and y...

I was reading about Weyl Transformations in Polchinski's book and I have a little doubt: Is it correct to say that under a Weyl transformation the scalars are invariant, i.e., that a weyl transformation preserves the scalar product?