Vectors Definition and 1000 Threads

I'd like to show why a 3-vector ##v## transforming using a quartenion ##q## must transform as ##v' = q^{-1}vq##. I tried showing that ##v^{\dagger}v = v'^{\ \dagger}v'## as long as ##v'## is given by the above transformation, whereas ##v' = qv## doesn't transform such that the inner product is...

In mechanics, a vector is represented by complex number (x + i y). Is there a simple/intuitive explanation as to why the y component is multiplied by i , which is equal to square root of -1 ? ; In this case, did it have to be of value sqrt(-1) ? or is "i" used to keep x and y separate and not...

Homework Statement At one instant a bicyclist is 20.5 m due south of a park's flagpole, going due east with a speed of 14.1 m/s. Then, 3.95 s later, the cyclist is 36.3 m due west of the flagpole, going due north with a speed of 18.3 m/s. For the cyclist in this 3.95 second interval, find each...

Do we have any proof to show that we can represent the addition of two vectors like this, i mean do we have proof for triangle law of vector addition(or its a law that is why we can't have its proof, then please give me a satisfying reason for this)

Homework Statement If vector a is added to vector b, the result is the vector c = (7.00, 3.00). If b is subtracted from a, the result is the vector d = (−4.50, 9.25). what is the magnitude of a? what is the magnitude of b? Homework EquationsThe Attempt at a Solution a + b = (7.00, 3.00)c...

For some reason I'm really struggling to get a correct answer on this problem "A horizontal clothesline is tied between 2 poles, 20 meters apart. When a mass of 3 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters. What is the magnitude of the tension on the...

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...

Homework Statement Vector A: 1.96N at 20° Vector B: 1.71N at 65° There are different parts I did the graph part by hand. I am having trouble finding it analytically. We have to use cm for our triangle. Homework EquationsThe Attempt at a Solution Vector A: 1.96 cm at 20° Vector B: 1.71 cm at...

<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...

Homework Statement Two cylinders, each with a mass of 10kg, are lying on an L profile. Neglect the thickness and weight of the L profile. Calculate the reaction force in b and e. Homework Equations G = mg The Attempt at a Solution So I tried to make a free body diagram of the cylinders. I...

Homework Statement [/B] For the vectors A and B (shown in the figure attached), carefully sketch: - The vector sum C = A + B - The vector difference D = A - B - The vector E = -A - B - The vector difference F = B - A Homework Equations Please explain how to do this. The Attempt at a...

Homework Statement [/B] Sketch in a third vector, C, whose magnitude and direction are such that A+B+C=0. Vectors A and B both have a magnitude of 5 and form a 30 degree angle (image attached).Homework Equations [/B] How do I go about this question? I have no idea how to start or what to...

Hello! I am reading some introductory differential geometry and they define the vector space associated to a point of a manifold as the tangent plane at that point. Intuitively it makes sense to call these vectors (just as the speed is the tangent to the trajectory), but why are those called...

Hello Everybody, A trapper walks a 6.2 km straight-line distance from the cabin to the lake, beginning to the lake has an angle of +45 degrees. Determine the east and north components of her dispacement vector. Work: E component: $6.2\times\cos\left({45^{\circ}}\right)$ = 4.38 N...

Homework Statement :[/B] Draw the vectors: A.) 60 lbs at 25 degrees east of north. B.) 40 lbs at π/3 south of west. Homework Equations [/B] I've tried different things but keep getting the wrong answer. Can someone please explain how to solve these types of problems?The Attempt at a Solution...

Homework Statement Question: A body of mass M1=m moving with a velocity V1=v in the x-direction collides with another body of the same mass m2=m moving in the y-direction with the same speed V2=v The coalesce into one body during collision Homework Equations (a) Find the magnitude of the...

Homework Statement show that points P, Q and R are in a straight line P (1, -3, 4) Q ( 2, 2, 1) R (3, 7, -2) and find the vectors ## \vec{PQ} ## and ## \vec{QR} ## Homework EquationsThe Attempt at a SolutionIn proving that the points are in a straight line, we might be able to use dot product...

1. The problem statement, all variables, and given/known data Triangle ABC has a point D on the line segment AB which cuts the segment in ratio AD : DB = 2 : 1. Another point E is on the line segment BC, cutting it in ratio BE : EC = 1 : 4. Point F is the intersection of the line segments AE and...

Homework Statement Two aircraft approaching an aircraft carrier are detected by radar. The first aircraft is at a horizontal distance of 34.3 km in the direction 42 deg north of east. and has altitude 2.4 km The second aircraft, at altitude 1.2 km, is at horizontal distance of 42.6 km in the...

ok don't know the book answer but think this is ok suggestions welcome:cool: $\tiny{t12.3.11}\\$ $\textsf{Find the angle between vectors}$ \begin{align*}\displaystyle u&=\sqrt{3i}-7j\\ v&=\sqrt{3i}+j-2k\\ u \cdot v&=(\sqrt{3})(\sqrt{3}) + (-7)(1)+(0)(-2)\\ &=3-7+0\\ &=-4 \end{align*}...

Homework Statement Homework Equations a^2+b^2=c^2 c^2=a^2+b^2-2abCos(theta)The Attempt at a Solution I'm having trouble trying to draw out the vectors. This is my attempt. I feel like it is wrong. Can someone help out please? Also, I'm not sure where to go from here... If I used...

$\tiny{hcc8.12}$ $\textsf{Find the sum of vectors $(10, \, 45^o)$ and $(7, \, 150^o)$}\\$$\begin{align*}\displaystyle \textsf{magnitude} &=\sqrt{(10\cos45^o - 7\cos150^o)^2 + (10\sin45^o - 7\sin150^o)^2} \approx 12.114 \end{align*}$ ok an online vector sum calculator returned 10.619 so...

I've read that if a given spacetime possesses a timelike Killing vector, then it is possible to define a unique vacuum state by constructing positive and negative frequency modes with respect to this timelike Killing vector. My question is, what does this mean? Explicitly, how does one use a...

A certain planet has a vector (Recl, L, B). The Earth and Sun vector exists on ecliptic. I need to know how to calculate the compound angle between the planet vector and the Earth-Sun vector.

I have posted this in University linear algebra, but it is possible there is a simple answer for this and the the problem belongs in some other forum. I apologize if that is the case. I am starting with 3 points in 3 space, along with the centroid of the full data set. The data is in principle...

Homework Statement Homework EquationsThe Attempt at a Solution The two particles are supposed to move along the same line. And the two radius vector could be anything. Is this correct?

I saw this thread "https://www.physicsforums.com/threads/electric-fields-magnitude-and-direction.765309/" If i understand this concept better now: E1 is facing opposite its source at +3 nC because it is a positive charge and the field flows out from the charge whereas -5 nC's vector points...

Homework Statement A ship traveling 55 degrees [W of N] is 65km farther north after 3.0h. What is the ship's velocity. Homework Equations sin, cos, tan? The Attempt at a Solution I know that Vground= Vair + Vwind, and that Vground = Vboat + Vcurrent, but I'm not sure if that is even relevant...

I have tried to find the three Killing vectors for the metric $$ds^2 = dr^2 + r^2d \theta^2$$ that is, the Euclidean metric of ##\mathbb{R}^2## written in polar coordinates. I found these to be $$\bigg(\text{first}\bigg) \ \ \xi_r = \text{Cos} \theta \\ \xi_\theta = -\text{rSin} \theta \\...

Hi all, Suppose we have vectors coming in order as A, B and then C (but A must be deleted before C comes in). Then how to get the dot product between A and C? It is allowed to store some calculations of A before deleting elements of A, for example, we could store norm of A, dot(A, B) and etc...

Homework Statement From Analytical Mechanics by Grant R. Fowles & George L. Cassiday. Only problem I am having is with part d. Homework Equations ##A\cdot B = A_xB_x+A_yB_y+A_zB_z## ##sin(\theta) = \frac{|A\times B|}{AB}## The Attempt at a Solution I did it by hand but also ran the following...

Homework Statement : [/B] r vector = 3t i + (4t-5t2)j. Find the angle made by the vector with respect to the x-axis and the y-axis. 2. Homework Equations : A.B=AxBx+AyBy 3. The Attempt at a Solution : I tried to take the dot product of the unit vector along x-axis and r. I did the same...

Homework Statement Hi, can you guys please see if my solution is correct. Any feedback would be awesome. Using components determine the sum of a + b if a = 3 m [N 30° W] and b = 2 m [N 10° E]. Homework Equations N/A The Attempt at a Solution

Homework Statement Hi Guys, I am a bit unclear regarding adding vectors and hoping someone can clear up the confusion for me. In the image below, we are adding two vectors and we used the vector components to find find x and y. Finally we then used x and y to get the resultant and the angle...

Hi everyone, I am taking my finals next week and I am really excited. But I forgot how to solve problems like these I know I'm supposed to separate them and solve for x and y seperately but its still not ringing any bells. Vector L is 303m long in a 205* direction. Vector M is 5552 m long in a...

I need help finding the coordinates of point B. I have the answer from the textbook but I have no clue how they got it. I also cannot go any further until I solve it. Note: I am studying at home so I have no lectures to go to for help. Questions is 3.4...

Homework Statement A mass of 20 kg is suspended from a ceiling by two lengths of rope that make angles of 30° and 45° with the ceiling . Determine the tension in each of the strings. 2.Relevant equations Fg= mg The Attempt at a Solution Fg= 20 x 9.8 = 196 N ∑F= fnet=ma Fg-FTtotal= 0 196=...

Homework Statement Ex. 2. Express each of the following by an equation: (a) Two vectors A and B are parallel. (b) Three vectors A, B and C are co-planar. Homework Equations C = A + B 3. The Attempt at a Solution I understand (a) the answer being B = (alpha)*A because that is a scalar...

Why is a vector's parity +1 and pseudo vector's parity -1 ? While it is the opposite case for scalars.

Hiya, I have a question in high school math, vectors to be precise: The point K(3.5,-0.5,-2) is the intersection point of the plane S1: mx-7my+5z+3=0 with the line l1: (n,1,-2)+t(-1,1,0) a) find the parameters n and m b) find the equation of the plane that contains the line l1 and is...

Homework Statement : [/B]Determine the resultant of three vectors of magnitude 1, 2 and 3 whose directions are those of sides of an equilateral triangle taken in order.Homework Equations : [/B] R2 = A2 + B2 + 2 A B cos θ tan α = B sin θ/(A+B cos θ) The Attempt at a Solution :[/B]...

Homework Statement Let A = (1,2,5) and B = (0,1,0). Determine a point P of the line AB such that ||\vec{PB}|| = 3||\vec{PA}||. Homework EquationsThe Attempt at a Solution Initially, writing the line in parametric form\vec{AB} = B - A = (0-1,1-2,0-5) = (-1,-1,-5)\\ \\ \Rightarrow \vec{v} =...

Hi all, I am currently self teaching physics and have come across something i don't know how to do. There are 2 cars, Cars 1 and 2, traveling at a velocity of 60km/h (16.67m/s) in the eastern direction with a gap of 5 metres between each other. Car 2 is in front of Car 1. Car 2 decelerates to...

I have 2 vectors: a = 1.0e-04*[0.110000000000000 0.140000000000000 0.140000000000000 0.140000000000000]; b = [0.000011000000000 0.000014000000000 0.000014000000000 0.000014000000000]; by look at by eyes, it seems similar; but when I use this command: a == b then I got...

I am a little confused about the difference between between coordinates and vectors. For example, when first studying vector calculus, you learn about vector fields, which formally are maps ##f: \mathbb{R}^n \to \mathbb{R}^n##, and we say that the function associates to every point in space a...

Homework Statement If the centripetal force is at the left side of the equation; that means if we move it over to the other side, it'll have a negative sign, which means it is opposite in sense in relation to N and mg. But how is that possible, considering that the centripetal force always...

Lets suppose we have a two vectors where ##\vec u=c\vec r## where c is just a reel constant number.Can we say ##\vec u## and ##\vec r## is parallel. How can we define ""parallel" vectors ? Like in most general way. I know that when c is positive real number they are definately...

Homework Statement In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite of the three pulls. Alex pulls with force \vec{F_A} of magnitude 220~N, and Charles pulls with force...

Homework Statement I have a vector V with components v1, v2in some basis and I want to switch to a new (orthonormal) basis a,b whose components in the old basis are given. I want to find the representation of vector V in the new orthonormal basis i.e. find the components va,vb such that |v⟩ =...

Hi, what does it mean to cross multiply two vectors? I couldn't imagine them in real life. eg Force vector. Multiplying Force vector to a scalar value means you multiple the 'Strength' of the force, Dot multiplication of Force with displacement to get work, means you get the work in...