Vector addition Definition and 182 Threads

so I've made some progress to this endeavour and come up with this to calculate Vector Addition; a weight averaged with a bias $$\frac { \sum_{n=1}^{N} \theta_{n} \cdot M_{n}{}^{X_n}} {\sum_{n=1}^{N} M_{n}{}^{X_n}}=\theta_{t}$$ I do have a round about way to figure out the Bias, ##X_n##, but...

Can we write for two different current density vectors : $$\vec J=\vec J_1+\vec J_2?$$ If we can, which is what I suspect, will it also not mean that the respective currents add up vectorially? Integrating the current densities above ##\displaystyle{\left(i=\iint_S\vec J\cdot d\vec a\right)}##...

Here is my code thus far and it seems to work (I've attached a gif as well so hopefully that works) va1 = [50*cos(pi/3), 50*sin(pi/3)]; %Two different vectors both starting from the origin vb1 = [20*cos(pi/6), 20*sin(pi/6)]; iterator = linspace(1,100,100); %100 iterations for the animation...

okay so I'm a Electrician I've found short method of calculating the final magnitude of a system (Lₜ), this relies mainly on Eucliud's axiom of angles within parrallel lines and is this ∑(cos(θₙ-θₜ)⋅Lₙ)=Lₜ where Lₙ and θₙ are the initail manignitude and angles respectively, and θₜ is the final...

Mentor note: Moved from General Math section, so is missing the homework template. If you want the vector which represents the base from 1 to 2 (or O1 to O2 are the position vectors, I am using co-ordinates as names), what would O12 (vector from 1 to 2) and why? 1. Would it be O1 - O2 or O1 +...

An airplane has an air velocity of 500 km/h [N 30 E] and encounters a wind from [S 75 W] at 180 km/h, find the ground velocity. Make sure you draw a big, labelled diagram. Please help! I’m understand the calculations that need to be done (cosine law then sine law for the angle) but I’m a little...

Hello, guys. Interesting riddle here. I have no idea how to solve it. Tried different methods, but point is answer is always wrong, exact answer Downriver, at an angle of 53.13(degree) to the bank. That exercise is from "Pohl’s Introduction to Physics"

I am following along with an example in my book regarding force from an electric charge. I understand the process but I believe I am getting something wrong when it comes to adding the vectors. Essentially, F13 is equal to -1.35*10^-3 j and when I add that to the j component of F23 which is...

Problem statement : While the statement is given above, I draw the given image for the problem. Attempt : It is clear at the outset that, since the velocity of river is constant, the man will not take the same time for the forward and reverse journeys. For both journeys however, the Relevant...

Could I please ask for any help with the following question: Here's my attempt: (i and j are unit vectors in the directions of east and north respectively) (apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram) Let the...

Hello all, In high school physics, the magnitude sum of vector addition can be found by cosine rule: $$\vec {R^2} = \vec {F^2_1} + \vec {F^2_2} + 2 \cdot \vec F_1 \cdot \vec F_2 \cdot cos ~ \alpha$$ and its angle are calculated by sine rule: $$\frac {\vec R} {sin ~ \alpha} = \frac {\vec F_1}...

Hello! I am reading about spin-orbit coupling in Griffiths book, and at a point he shows an image (section 6.4.1) of the vectors L and S coupled together to give J (figure 6.10) and he says that L and S precess rapidly around J. I am not totally sure I understand this. I know that in the...

Hi everyone, While finding the solution for one of my exercises, I found the following answer. I'm seriously questioning if the equations provided in that answer are reversed. According to my understanding, if two vectors ##\vec{S}## and ##\vec{T}## are parallel (same direction) the magnitude...

i know its pretty basic but please give some insight for triangle law of vector addition and pythgoras theorem. becuase ofcourse if you use traingle law to find resultant it will be different from what is pythagoras theorem

I am writing about the nature of force in classical mechanics and what does really imply, in terms of change in motion. I am using as an example a circuit, on which we exert a force. I am trying to justify the following scheme (concretely, ##f_{mag}##): The thing is that I am wondering how...

Im really stuck with this problem ! any help would be much appreciated

Homework Statement Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that |u|=√2, |v|=√3, u is perpendicular to v, w=u×v. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ The Attempt at a Solution [/B] Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...

Problem: Dr. L and his cat Kepler are coming home from fishing. They ended their trip on the south bank of a river, directly across a 1200 m wide river, from where Caroline was going to pick them up on the north bank. They are in identical boats that can travel at 4 m/s (Vb). The river is...

Please see the attached page to see what I'm talking about. In the top right paragraph, it states to use "the positive direction of the x-axis". It is given that ##θ_2=30°## and it shown visually at the bottom of the page. In the problem it's using -60° and I'm not sure how they're getting that.

Take some sort of system accelerating with respect to an inertial reference frame: let's take a spherical mass on the end of a string forming a simple pendulum with the ceiling of a car, and allow that car to accelerate uniformly. Could someone share with me how they interpret the concept of a...

Homework Statement Give an example of the associative property of vector addition using vectors in Cartesion form. Homework Equations (u+v)+w=u+(v+w) The Attempt at a Solution I can't figure out how to get the arrow on top of my work so I wrote it without it. I'm somewhat confused on why I...

Homework Statement "A bird flew 40 m to the west, then 100 m in a direction 36.9 degrees to the north of east. Use the algebraic addition of vectors to fins the magnitude of the bird's net displacement" Use sin (36.9) =0.6 and cos (36.9) = 0.8 Homework Equations Vector addition? A =...

Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? Homework EquationsThe Attempt at a Solution I tried using the dot product and solving for the angle but i...

I just want to know the difference between those rules: 1. R^2 = F1^2 * F2^2 + 2*F1*F2*COS(the angle between F1 and F2) 2. The second is about the parallelogram rule, it says that the two vectors are added and their summation is the magnitude of the resultant. Which one is correct?

Homework Statement A man wishes to cross a river of width 120 m by a motorboat. His rowing speed in still water (or relative to water) is 3 m/s and his maximum walking speed is 1 m/s. The river flows with a velocity of 4 m/s. (a) Find the path which he should take to reach the point directly...

Homework Statement A pilot wishes to fly at maximum speed due north. The plane can fly at 100km/h in still air. A 30km/h wind blows from the south-east. Calculate: a) The direction the plane must head to fly north. b) Its speed relative to the ground. Homework Equations Sine Rule...

I know that n-body problem can be complicated, but that's for the dynamics. What about a static case: e.g. if I have the distances of several bodies A, B and C etc. and their distance to a reference mass m, can I just use the vector addition of the Newton's gravitational force to add up all of...

Homework Statement >There are three vector $$ \vec a ,\vec b, \vec c$$ in three-dimensional real vector space, and the inner product between them $$\vec a . \vec a=\vec b.\vec b=\vec a.\vec c=1, \vec a.\vec b=0, \vec c.\vec c=4 $$ When setting $$x = \vec b.\vec c$$ , (dot here means dot...

Homework Statement A river of width 4 km flows at 5 km/h. A swimmer whose speed relative to water is 4 km/h, starts swimming from a point A on a bank. What minimum distance will the swimmer have to walk on the other bank to reach point B directly opposite to A? [/B]Homework Equations Vba = Vb...

Homework Statement Hello, I am currently studying mathematics and physics on my own, and I ran into a type of problem in physics that is a bit unclear to me. Say we have pulley at the top of an inclined plane with a base angle of alpha and the top angle is alpha. Homework Equations I assume...

Homework Statement Given that vector a = (1, 2, -5), b = (-12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0 Homework Equations No specific equations, as the question asks for the value without making any calculations. This problem...

Homework Statement Given the following diagram, use vector addition to sketch the resultants: a) u→−2v→ b) 3v→−u→ Homework EquationsThe Attempt at a Solution For this question I am fairly certain that it is correct but for some reason I'm doubting myself. I was wondering if I could get some...

Homework Statement I have an exam on vectors and 2 dimensional motion today. I NEED to know if it is possible to solve any GRAPHICAL VECTOR PROBLEM using only INTEGRATION AND MATH WITHOUT ADDING VECTORS TOGETHER GRAPHICALLY. So given any word problem that is supposed to be solved using that...

Homework Statement Vector A + Vector B + Vector C = 0 A=B+C Homework Equations Find the angle between vector A and vector B The Attempt at a Solution I tried to solve this problem by resolving all the vectors and individually equating the value of vectors at each axes x, y and z to 0 but got...

Homework Statement Vector A: 1.96N at 20° Vector B: 1.71N at 65° Homework EquationsThe Attempt at a Solution I change the Newtons to cm. Vector A: 1.96cm and Vector B: 1.71cm. I multiplied it by 2 so it would look bigger on the graph paper. Vector A: 3.92cm and Vector B:3.42cm. I was able to...

<Moderator's note: Moved from a technical forum and therefore no template.> Homework Statement A proton (q = 1.60 x 10-19) is in a uniform, 0.500 T magnetic field. This proton has velocity components vx = 1.50 x 105, vy = 0, and vz = 2.00 x 105 m/s. Find the force on the proton at t=0. 2...

I've been racking my brain for a while now over what I feel should be a simple problem to solve, but my answer is wrong. I'm not wildly wrong, but wrong enough to think I've made a proper error and it's not just a rounding error or something. The question goes like this: A dog in an open field...

Homework Statement As part of a longer problem: "Find necessary and sufficient conditions for the point with positionvector r to lie inside, or on, the tetrahedron formed by the vertices 0, a, b and c." Homework Equations I am not sure... vector addtion? The Attempt at a Solution I don't...

Homework Statement Homework Equations N/A The Attempt at a Solution [/B]

Homework Statement A train is traveling east along a straight run of track at 72.0 km/hr. Inside, two siblings 1.9 m apart are playing catch directly across the aisle. The kid wearing a P.J.Harvey T-shirt throws the ball horizontally north. The ball crosses the train and is caught 0.75 s later...

Does he make a mistake at 6:18? In case of associativity. When doing a+(b+c) he's just placing the tip of a to the tail of (b+c), but shouldn't he have added the tail of a to the tip of (b+c) ending in a different point? I understand vector addition is associative, but I think how he did it is...

Acording to this diagram vector P = vector BC and vector Q = vector OB(their magnitudes are also respectively equal.) Therefore acoording to the congruency of triangles angle alpha = (theta)/2. But this is not right( what's wrong ) {Tan(alpha) = Qsin(theta)/(P + Qcos(thets)) ] Why resultant...

Homework Statement A car with a mass of 1400 kg is westbound at 50 km/h. It collides at an intersection with a northbound truck having a mass of 2000 kg and traveling at 40 km/h. What is the initial common velocity of the car and trucks after collision if it's an inelastic collision? Homework...

i have two unitary vectors in space U and V , U and V are perpendicular . W is a vector that verifies W ^ V = U - W . the following resolution is incorrect , i wan't to understand why : we use (o,U,V,(U^V)) . components of U (1,0,0) , V(0,1,0) , W(a,b,c) where a , b and c are real...

Homework Statement two people kick a ball. one of them kicks it with a force of 215.0 Newtons. the other one with 189.0 Newtons. their approach creates a 210.0 degree angle at the point of impact and causes the ball to go in a different direction. what is the resultant of the vector from this...

Homework Statement You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north. 1) What is the speed of the plane with respect to the ground? Homework...

Homework Statement [/B] Given the following vector components of vectors C and D: Cx = 8.10, Cy = -5.40, Cz = -7.90, Dx = 4.40, Dy = -2.50, Dz = 4.50, find the x, y, z components of their sum. Homework Equations No relevant equations that I know of...[/B] The Attempt at a Solution I am...

Homework Statement Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is flying at 100 km/h relative to the air but a 38 km/h -km/h wind is blowing from west to east. At what...

Homework Statement In photo: https://gyazo.com/6348b5ffe368852ee9868a2ba0dd7e38 Homework Equations In image The Attempt at a Solution In the boxes Where did I go wrong with the angle calculation? Thanks

I don't need help finding the resultant of this example problem. What I do need help for is: What exactly from this prompt hinted that I must add all the vectors provided. I have read this many times through and I still didn't know what to do. How does adding the vectors help them find the...