Vectors Definition and 1000 Threads

Homework Statement Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...

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...

What's the difference between saying that a vector's direction is north of east and north east?

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you don't see image here is the matrix which is 2X2 in MATLAB code: [9/25 12/25; 12/25 16/25] Homework...

Homework Statement x = <0, 10, 0> v1 = <4, 3, 0> v2 = <0, 0, 1> Project x onto plane spanned by v1 and v2 Homework Equations Projection equation The Attempt at a Solution I took the cross product k = v1xv2 = <3, -4, 0> I projected x onto v1xv2 [(x*k)/(k*k)]*k = <-4.8, 6.4, 0 = p I finished...

Homework Statement - Question: Which cyclist (A, B or C) profits the most from cyclist slipstream (also called “aerodynamic drafting”)? - Given: the direction of the wind, the positions of each cyclist; an illustration representing this - NOTE that I am expected to solve this question...

Homework Statement A force of magnitude 50N is applied at the bottom point Q of a disk of radius 8m that is pinned at P (leftŸmost point) See attached picture (a) Find the angle between the force and the vector from P to Q. (b) Find the magnitude of the applied torque. Homework Equations...

Imagine an aircraft of which the its wing is connected to its landing gear by means of a hinge (joint), and then the gear suddenly gets stuck midway. If, subsequently, the aircraft makes a turn around its longitudinal axis (see picture), it seems to hold true that then the angle between the...

Hi, If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or...

Homework Statement I am asked to write an expression for the length of a vector V in terms of its dot product in an arbitrary system in Euclidean space. Homework EquationsThe Attempt at a Solution The dot product of a vector a with itself can be given by I a I2. Does that expression only apply...

Homework Statement Refer the given image. [Prob 2.9] Homework Equations F=ma The Attempt at a Solution I drew the normal vector perpendicular to the surface of the cone and resolved it as ##Nsin\theta=mg## ##Ncos\theta=\frac {mv_{0}^2} {r}## where ##v_{0}## and ##r## are the speed and radius...

Homework Statement Homework Equations Trigonometry equations, p=m/v, A = pi * d^2 / 4 The Attempt at a Solution i) mass calculated is 9.318kg at 150° from A ii) diameter = 0.235m I apologize for the messy working, I am just wondering if I have followed the correct procedure or not...

I have a Force Vector = 100N, making an Angle = 45 degrees with x-axis. When I find their Components trigonometrically, I get 70N each; as Fx = 100xCos(45) = 70N Fy = 100xSin(45) = 70N Verifying the result, by Head-to-Tail method, I get 70N + 70N = 140N. Why is there discrepancy or where am I...

Homework Statement Homework Equations definition of null vector, [/B] The Attempt at a Solution null vector : ## |0 \rangle = (0,0,0) ## inverse of (a,b,c) = ( - a, -b, -c) vector sum of the two vectors of the same form e.g. (c,d,1) + ( e,f,1) = ( c+e, d+f, 2) does not have the same...

Given two probability distributions ##p \in R^{m}_{+}## and ##q \in R^{n}_{+}## (the "+" subscript simply indicates non-negative elements), this paper (page 4) writes down the tensor product as $$p \otimes q := \begin{pmatrix} p(1)q(1) \\ p(1)q(2) \\ \vdots \\ p(1)q(n) \\ \vdots \\...

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate the fingers in the direction of motion of the rotating body then thumb will point the direction...

Homework Statement This is a solved problem, but I haven't understood a few things. I've marked out sections of the solution in white for convenience. The markings are positioned where that particular section ends. In part (1), how did they just assume f1(0) = 2, f2(0) = 3, g1(0) = 3, g2(0)...

A very simple question. How do we represent a vector with Newton's notation (writing the arrow symbol with the overdot notation)? Can we write them both above each other. First, the overdot notation and then the arrow symbol? Thank you a lot for your help...

According to the vector definition, the vectors have both the direction and magnitude such as displacement vectors which should possesses arrows on the top of them because they have displacement so they express a direction. On the other hand, position vectors are stationary, they do not have any...

Homework Statement Given ##a\neq b## vectors of ##\mathbb{R}^n##. Determine ##c## which lies in the line segment ##[a,b]=\{a+t(b-a) ; t \in [0,1]\}##, such that ##c \perp (b-a)##. Conclude that for all ##x \in [a,b]##, with ##x\neq c## it is true that ##|c|<|x|##. Homework Equations The first...

Homework Statement Homework Equations Is my solution correct? If not then please point out the mistakes and help me solve this question in the right way. Thanks in advance. The Attempt at a Solution

Homework Statement What is the sum of position vectors of all points on a circle? Don't use Cartesian system. Homework Equations Sum vector $$\vec s = \int_{\theta=0}^{\theta=2{\pi}}\int_{r=0}^{r=R} \, \,\vec P \, dr d\theta$$ where $$\vec P$$ is the position vector. The Attempt at a...

Homework Statement Imagine there exists reference two frames, a frame O which is stationary and another, O' moving relative to O. If there is a four vector A--> (A0,A1,A2,A3). Then why is Aae->a as measured by the observer O equal to Aa'e->a' as measured by the observer O'? The components are...

Homework Statement In most problems involving projections I'm given a vector and the equation of a line either in parametric form or in symmetric form (ie. parametric: <0t+3, -t-4. 3t+2> or symmetric form: x=3, (y+4)/-1, (z-2)/3). However, when asked to use these in a problem I get confused...

Hi everybody, I have a problem with this question: Choose from the following set of vectors in R4 set of the maximum number of linearly independent vectors: 1.(1;2;3;4) 2.(2;4;6;8) 3.(0;1;-1;1) 4.(1;1;1;0) 5.(0;3;0;0) So, I can find a rank of a matrix, it's 4, but I can't understand how it...

Homework Statement [/B] Homework Equations The Attempt at a Solution [/B] I am not sure if this is the correct way of finding the difference between two vectors. I thought that if "B" was negative then it's direction would change as well as it's angle. If the angle changes then are my...

So I'm reading through some stuff trying to learn tensors, and I wanted to stop myself to grasp this concept before I go further. Along the way it was mentioned in one of the sources I'm looking at that other than the dot product and cross product, you could multiply vectors in another way, and...

I've been reading up on Killing vectors, and have got on to the topics of homogeneous, isotropic and maximally symmetric space-times. I've read that for an isotropic spacetime, one can construct a set of Killing vector fields ##K^{(i)}##, such that, at some point ##p\in M## (where ##M## is the...

Homework Statement I am unsure as to how the partial derivative of the basis vector e_r with respect to theta is (1/r)e_theta in polar coordinates Homework EquationsThe Attempt at a Solution differentiating gives me -sin(theta)e_x+cos(theta)e_y however I'm not sure how to get 1/r.

An airplane is flying on a bearing of South 27degrees West at 485 mph. A 35 mph wind is blowing from a direction of South 72degrees East. What is the actual bearing of the plane and the ground speed of the plane? I've been stuck on this problem for so long and am going to ask for help

I am trying to understand the solution to exercise 7.10(e) on pages 175-176 of Robert Scott's student's manual to Schutz's textbook. He writes the following: I don't understand how to find ##S^x, S^z## or ##T^x,T^z## from the metric or from the cartesian representation of the rotation...

So, if kinematics is the study of motion without reference to its causes (which is how it seems to be defined in many places), then here is my attempt to come up with a complete picture of motion without reference to its causes. This is just a summary to help me organize my thoughts (it is NOT...

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 I don't understand how to form an equation using the knowledge that, 'When ##t=4##, ##P## is moving parallel to the vector ##\mathbf {j}##'. I've seen the solution, and not a single part of it makes sense. I haven't attempted any question like this before, so I have no idea...

Please can anyone help with: a plane has speed in still air (no wind) of 40kmh-1 and is traveling in a direction of 65 degrees bearing but there is a wind blowing at a speed of 20kmh-1 from the south east. If I is east and J is north, express the velocity p for the plane in no wind and velocity...

Homework Statement |a| = 2 |b| = ## \sqrt3## |a - 2b| = 2 Angle between a and bHomework EquationsThe Attempt at a Solution ##\theta## is angle between a and b So angle between a and -2b is 180-##\theta## [/B] ##|a-2b|^2## = |a|^2 + |2b|^2 -2|a||2b|cos(180-##\theta##) ##2^2## = 2^2 +...

I ran across the explanation below of a car on a banked turn (no friction) on a High School teacher's website. I'm assuming this is incorrect, because how can the normal force in this situation equal mg/cos when an object on an inclined plane has a normal force equal to mg * cos? The high...

Hi, I've got this problem I'm trying to work out. The problem seems simple, but I don't think I have a good way to construct a way to solve it. This is the problem. Let P and Q be two points with position vectors p and q and let R be a point midway between these two. Find an expression for the...

I read from this page https://properphysics.wordpress.com/2014/06/09/a-no-nonsense-introduction-to-special-relativity-part-6/ that the basis vectors are the canonical basis vectors in any coordinate system. This seems to be wrong, because if that was the case the metric would be the identity...

This problem is fairly objective (though quite stupid) What does î(o) represent? Does it refer to a vector making angle 0 degrees with the x axis? I searched but couldn't find the answer anywhere. Please help. Moderator note: post edited and moved from hoemwork

Hi physicsforums, I am an undergrad currently taking an upper-division course in Quantum Mechanics and we have begun studying L^2 space, state vectors, bra-ket notation, and operators, etc. I have a few questions about the relationship between L^2, the space of square-integrable complex-valued...

Homework Statement Homework EquationsThe Attempt at a Solution I am having a bit of trouble visualizing the vectors for these type of problems. The angles they give are very ambiguous and so I am not sure why they are there. For the 45 degree angle, how do i know that this is used for finding...

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 Describe how the dot product can be used to determine whether two vectors are perpendicular. Create a question with vectors in 3-space to illustrate this property. Solve the question as well. Homework EquationsThe Attempt at a Solution Did I do this right? I did something...

Homework Statement Given two vectors u→=(16,5,2) and v→=(3,−2,−2) find the following: The coordinates of the projection of u→ on v→The magnitude of the projection of u→ on v→ . Homework EquationsThe Attempt at a Solution I have never done a question like this before, I was curious did I do...

I recently had a test question where I had to calculate a force on a charged particles from two other charges particles. The answer ended up having an x and a y component. I realized I wasn’t quite sure how to represent that vector. Should I just have written it as something like 5Nx^ + 6Ny^...

Homework Statement A(-4,-4), B(4,-2) and D(-2,2) a) Determine AB and AD vector My answer: AB=[8,2] and AD=[2,6] b) A point C is determined by DC being parallel to AB and the angle ABC = 90. Calculate the coordinates of C. I found out that C=(46/17, 54/17) c) Another point E has the...

As far as I know, vectors can only be added, subtracted, or “multiplied” by dot or cross product. Does this mean that you couldn’t divide f-> by a-> to get m using the vector form of Newton’s second law? This would require dividing a vector by a vector, which seems to not be allowed.

Hello Everyone. I am searching for some clarity on this points. Thanks for your help: Based on Schrodinger wave mechanics formulation of quantum mechanics, the states of a system are represented by wavefunctions (normalizable or not) and operators (the observables) by instructions i.e...

Homework Statement Show that {(1, 2, 3), (3, 4, 5), (4, 5, 6)} does not span R3. Show that it spans the subspace of R3 consisting of all vectors lying in the plane with the equation x - 2y + z = 0. Homework EquationsThe Attempt at a Solution I made a matrix of: A = [ 1 3 4 ; 2 4 5; 3 5 6] and...