Dot Definition and 552 Threads

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...

Please Help Me Figure Out The Lewis Dot Diagram for NO+ (nitrosyl).

Homework Statement find velocity x dot, as function of time t, for particle mass m starts x=0, t=0 subject to force where Fo and c are constants. Fx = Fo + ct Homework Equations answer is x dot =Fo/m t + c/2m t^2 The Attempt at a Solution obviously it is just an...

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...

Vectors, dot products help! OK, I know this is probably really annoying but I have a ton of questions. (I would go to the math tutor but they aren't here yet because the semester just started.) 1. Find the angle POQ by vector methods if P=<1,1,0>, O=<0,0,0>, and Q=<1,2,-2>. What I have...

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...

Lately I've noticed a black dot in the vision of my right eye (a few weeks now). I'm used to floaters, this is different - it's black. Other than that, it's much like a floater: it's out of focus and, while it seems to move around, I think that's just my eye movements (I don't see how it could...

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 =...

dot product and cross product. i (think dot product is like eg (1,2,4).(2,4,5) = 30 and cross product is like eg(1,2,4)x(2,4,5)=2, 8, 20) but I am not sure... and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right. but if left to right what's the rule in when...

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...

My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined inner product, and uses that to define the hodge dual. That wedge inner product definition was a determinant of inner products. I don't actually have that book on me right...

Homework Statement For x,y \in R^n, their inner ("dot") product is given by <x,y>=\sum_{i=1}^n x_i y_i. Also, we write <x,x>=\|x\|^2. Homework Equations Fix p>1. Show that for all x,y \in R^n we have < \|x\|^{p-2}x -\|y\|^{p-2}y, x-y> \geq 0The Attempt at a Solution Expanding the...

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...

Anyone familiar with dot products of two vectors? What does the dot product show, in other words what is the point of doing a dot product?

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...

This is something you might want to take a look before you go off on your next air travel in the US. http://www.powerpage.org/2007/12/us_dot_bans_transport_of_spare_lithium_batteries_in_checked_baggage.html This is going to be a bit annoying since we travel with spare camera and camcorder...

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) =...

Q:Given non-zero vectors u and v, find a vector x such that both equalitites x dot u=|u|, and x cross u = v hold. What should be the mutual position of the given vectors u and v in space, so that the problem has a solution? What I've got so far: Setting x = au + b(u cross v) I have that...

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...

ii think i did this correct ( i hate projections) Homework Statement find the scalar and vector projections of b onto a Homework Equations a= (-1, -2 2) b=( 3,3,4) scalr (a dot b)\|a| vector (a dot b)\|a| * a/|a| The Attempt at a Solution (a dot b)\|a| =(1 =6...

Homework Statement Ok so i ran into trouble in the momentum section because i do not understand dot products as well as i thought. I tried going back and revising my notes but nothing new comes to mind. Your help is highly appreciated. ok so let me just state that m1=m2 the problem...

If for a function space , we can define the scalar product of any given 2 functions as \int_{a}^{b}dx f^{*}(x)g(x) what happens with its analogue the 'dot/cross' (vectorial product of 2 vectors which is itself another vector orthogonal to the 2 given ones) the question is not in vane...

I can't seem to derive the law of cosines from the vector addition of C = A + B using the dot product. Does anybody have any insights?

Hello, I'm reading a classical mechanics book. In it, they show a derivation of the centrifugal force equation: \vec{ F_{\textrm{cf}}} = -m \vec{ \omega } \times \left( \vec{ \omega } \times \vec{ r } \right) I understood the derivation up to that point. However, they have a couple additional...

I just reviewed Dot Product, but I don't know what it actually, exactly means. would you tell me about its physical meaning or something interesting quality of it? Thanks

I have become exceedingly confused by the various sign changes involved in computing the electric potential produced by a charge distribution, and I am sure I am simply forgetting a negative sign somewhere and am going crazy. However, V = -int from infty to r of E . ds ds is the...

Need help with this problem. I need to show that one side equals the other. I this is distributive property but isn't that just too plain simple? I mean I am in pre-cal class and therefore this question can't be easy as it seems... ::biggrin: anyways, if anyone knows about vector plez help...

Homework Statement Draw out the electron dot diagram for isopropyl alcohol. Homework Equations C[SIZE="1"]3H[SIZE="1"]7OH The Attempt at a Solution Carbon = 4 valence electrons, multiplied by 3 carbons gives us 12 valence electrons for carbon. Hydrogen = 1 valence electrons, multiplied by...

Use two methods to determine a unit vector perpendicular to both (2,1,-3) and (-1, 7, 4) Using Cross Product: Let v be a perpendicular vector to the given vectors v = a*b = (2,1,-3)(-1,7,4) =((1)(4)-(7)(-3), (-3)(-1)-(4)(2), (2)(7)-(-1)(1)) =(4+21, 3-8, 14+1) =(25, -5, 15) = (5, -1...

I need to show: (\mathbf{\sigma} \cdot \mathbf{a})(\mathbf{\sigma} \cdot \mathbf{b})=\mathbf{a} \cdot \mathbf{b} I + i \mathbf{\sigma} \cdot (\mathbf{a} \times \mathbf{b}) where a and b are arbitrary vectors, sigma is the pauli spin operator. I was just wondering what the dot product...

An inertial reference frame 2 is moving along the x-axis with constant velocity v with respect to inertial reference frame 1. ......->-> ->-> How can i prove the E.H = E'.H' ?? (dot product) using the 4 dimensional (Ax,Ay,Az,phi) where E = -1/c dA/dt - gradiant(phi) and H = curl(A) Where E is...

Hi, I am not too sure about my lewis dot diagrams, can someone check them and let me know if anything is wrong with them, thanks.

I was wondering if anyone could give me information the base of cross product all the problems I have been reading about so far have been in real depth I need to understand the basics first the problems given here are the beginning, if anyone can give me any help please do so, and thank you in...

While taking linear algebra I never really understood where the dot and cross product came from. It seemed that they were just randomly defined. I know that the dot product is an inner product but why is it defined as: \vec v \cdot \vec u = v_1 u_2 + v_2 u_2 ? why not \vec v \cdot \vec u =...

Homework Statement Needan optical sensor to detect a dot sequence on widgets passing 50cm away from the sensor. Want each dot to exactly cover the sensor. If the dots are 10mm in diameter and the sensor is 40mm in diameter, what is the position and focal length of the lens to do the...

Hi I'm new here and I'm having trouble with this algebra question please help. Sorry if my latex is ugly I'm new to it. I get stuck at the bottom line and I'm not sure how to go further with the question to solve for K #7 - Angle between 2 vectors is \alpha where cos\alpha = \frac{3}{7}. a =...

Dears Is any method to calculate the density of states of spherical (purely) quantum dot?

Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...