Dot product Definition and 390 Threads

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...

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

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} =...

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...

Homework Statement http://img152.imageshack.us/img152/3851/33495448dh9.png Homework Equations http://img146.imageshack.us/img146/4655/37276835io7.png The Attempt at a Solution Well I found: ||f|| = \frac{1}{ \sqrt{3}} ||g||=\frac{i}{ \sqrt{3}} <f,g> =...

Is it possible to represent the dot product (matrix multiplication) with sums? For example, know the dot product of a polynomial and another one [i.e. 2+5x and 3x+7x2] would be the sums of the products. [i.e. 2(3x) + 5x(7x2)]. Could this be also written as \sum^{n}_{i=1} a1ibi1? I'm asking...

Questions about matrices and vectors: Why does the dot product of a and b equal |a||b|cos(angle between a and b) are the vectors of a matrix the columns or the rows, or can it be either? I know a 0 determinant of a matrix means the vectors lie on top of each other, and the absolute...

I guess one of them is scalor and one of them is vector, but what is the REAL DIFFERENCE between them? gracias

Homework Statement * With an axis system oriented as shown, the position vectors of points A and B are rA = 175i + 0j + 0k m rB = 39i + 70j + 29k m * When the trolley is halfway between points A and B, the forces exerted on the trolley by the cables are F1 =...

Hi, I have a question about dot product for vector. For detail : https://ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=st&chap_sec=02.4&page=theory Is there anyone understand about it and explain to me the basic concept, why : 1. A • B = |A| |B| cosθ, not A • B =A^2 • B^2 - 2AB cosθ...

Homework Statement 1. For the vector field F = yz ˆx + zx ˆy + xy ˆz (^x means the unit vector of x) find the integral of F • dl from (0, 0, 0) to (1, 2, 3) in Cartesian coordinates in each of the following ways: (a) along a straight line path from (0, 0, 0,) to (1, 2, 3) (b) along...

Homework Statement Show (A x B) dot (C x D) in terms of dot products only. Homework Equations A x B = ABsin(theta) A dot B = AB cos (theta) The Attempt at a Solution Subbing both those formulas into the top I got [ABsin(AtoB) times CDsin(CtoD) ] cos(between the two resultant...

I have a question concerning scalar invariance with respect to an accelerating and an inertial reference frame. Here is the problem. Suppose we have a rotating spherical object, which we denote as the rotator, attached to a near-massless wire. The other end of the wire slips loosely over a...

Homework Statement If |A+B|^2=|A|^2+|B|^2, prove that A is perpendicular to B. Homework Equations A^2=|A||A| The Attempt at a Solution All I can think of to do is expand the equation to get (A.B)(A.B)=A.A+B.B. I know that iff a.b=0, the two are perpendicular but I can't figure...

Given a function f: R^n -> R, a point x in R^n, and an arbitrary vector v in R^n - is the dot product between grad f and v (evaluated at x) the same as df/dv? If yes, it would be great if someone were to demonstrate a proof. If no, what should be the correct interpretation of the dot product?

If I differentiate two unit vectors, one with respect to the other, would it just be the dot product between the two vectors (namely the cosine of the angle between them)? I don't understand the physical meaning of the result...

there are 2 situations that need explanation. first, the general formula for electric potential as you take potential = 0 at infinity as a reference. Second, the general formula for capacitance on a parallel plate. In situation one, the negative sign does NOT DISAPPEAR, and in the second...

It began in class with this problem. Find the dot product of 2 vectors: v1 a vector with components <4, 8> v2 a vector of length 1 angle pi/4 So, i have 2 ways of doing it. 1) v1.v2 = v1x.v2x + v1y.v2y 2) v1.v2 = |v1||v2|cos(theta) And they should come out the same but. 1) v1.v2 =...

One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors? A dot B = ABcos(theta) 113 = 12*23*cos(theta) 113/276= cos(theta) cos^(-1)113/276 = theta 65.8 degrees or 66 degrees using...

True or False: The only way to get a negative dot product is to have an angle larger than 90 degrees. The formula is ABcos(theta) False because from 3pi/2 to 2pi the cos is positive and 3pi/2 and 2pi is larger than 90 degrees. Right? Stephen

Homework Statement Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 49° with each other. Find (vector A)(vector B) Homework Equations The Attempt at a Solution (5i+0j)(0i+9j)= (5N)(0m)+(0N)(9m)= square root...

ı need to learn how can ı calculate ' del . r (A . r) ' where 'A' is a constant vector , 'r' is a distance vector and '.' is dot product. the result must be 4(a.r)

Homework Statement 15) In Question 14, if the ramp makes an angle of 20 degrees with the level ground. Find the magnitude of the force tending to lift the crate vertically. Textbook Answer for Question 15: 108.3 N ---- 14) A crate is being dragged up a ramp by a 125 N force applies at an...

Homework Statement If d1 = 4i - 10j + 2k and d2 = 9i - 10j + 6k, then what is (d1 + d2) · (d1 × 4d2)? Homework Equations Know how to do the cross product and dot product The Attempt at a Solution For the answer i got 9.6i + 56j -127.68k. How do i express that as a scalar for an...

Homework Statement If you have two functions dependent on t, A(t) and B(t). Prove their derivatives are as follows: d(A (dot) B) / dt = [A (dot) (dB)/(d(t)] + [d(A)/d(t) (dot) B] {Where "(dot)" acts as the dot product} d(A x B) / dt = [A x (dB)/(d(t)] + [d(A)/d(t) x B]...

Find the three angles of the triangle with given vectors. A(1,0) B(3,6) C(-1,4) I found that AB & BC are congruent, so this ends up being an Isosceles triangle and the only angle I need to find is B. BC=<3+1,6-4>=<4,2> AB=<3-1,6-0>=<2,6> \angle B=\cos^{-1}{\frac{20}{\sqrt{20 \cdot 40}}=45^o...

Homework Statement A particle is located at the vector position =(5.00i + 7.00j) m and a force exerted on it is given by =(3.00i + 2.00j) N. (a) What is the torque acting on the particle about the origin? (b) Consider another point about which the torque caused by this force on this...

Does anyone know what the geometrical interpretation of a dot product in 3-D is? I am calculating the dot product between two vectors in 3d and need to use the |a||b|cos(theta) interpretation basically, but that is for 2d. Can I just tack on an additional cos(theta2)? Thanks a lot for your...

Homework Statement I get confused with this problems show that the vector (orth of b onto a) = (b - proj of b onto a) is orthogonal to a. Homework Equations The Attempt at a Solution (b-proj of b onto a) dot a = 0 and I got stuck!

Oh guys, I'm asking for explanations here, a little lesson. If something could explain vector dot product (including it's algebraic method) that would be great. And another thing, what is the difference between Gaussian and Gauss-Jordan elimination?

\overrightarrow r (t) is a vector valued function given by: \overrightarrow r (t) = x(t)\overrightarrow i + y(t)\overrightarrow j if h(t) = \left| {\overrightarrow r (t)} \right|, show that the following is true: \overrightarrow r (t) \bullet \overrightarrow r '(t) =...

This technically a homework question, but needed for homework and understanding for homework to come. Just hope to get it cleared up, thanks again! 1. This formula is given: r_{1}s_{1} + r_{2}s_{s}+ r_{e}s^{3} = \sumr_{n}s_{n} (with the limits etc. not too important). Then, in respect...