Unit vectors Definition and 138 Threads

I remember in my first year physics classes, when dealing with a force F we would find the vector's x- and y-components using F_x=r cos(θ) and F_y=r sin(θ) I also remember learning in my mathematics classes about unit vectors, but cannot seem to remember using them to break vectors down into...

Hey, everyone. I am going to post a question—but it's not the question I need help with. It's something deeper (and way more troubling). Consider a particle of mass m subject to an isotropic two-dimensional harmonic central force F= −k\vec{r}, where k is a positive constant. At t=0, we...

Homework Statement The Attempt at a Solution I already know how to do a), but what I am wondering is what the question means by expressing position in the terms of those unit vectors.

Find a two unit vectors that make the angle \pi/3 with the vector \vec{v} = \vec{i} + 2\vec{j} + 3\vec{k}. "That isn't asking much since there are apparently infinite such vectors" - Prof. I get as far as to say that \pi/3 = arccos( 1/2 ) and that \frac{v \bullet w}{|v||w|} = 1/2 but from...

I have two questions 1) How the radial and traversal unit vectors are vector funcitons of scalar variable θ (angle between the position vector and polar axis. 2) To find velocity and accleration in polar co ordinates why it is need to write the traversal and radial unit vectors by...

Hello, I'm studying The Theory of Polymer Dynamics by Doi and Edwards and on page 98 there is a tensor, defined as a composition of two identical unit vectors pointing from the monomer n to the monomer m: \hat{\textbf{r}}_{nm}\hat{\textbf{r}}_{nm} As far as I understood, the unit vectors...

I keep reading about polar unit vectors, and I am a bit confused by what they mean. In the way I like to think about it, the n-tuple representation of a vector space is just a "list" of elements from the field that I have to combine (a.k.a. perform multiplication) with the n vectors in some...

Homework Statement Find all the unit vectors orthogonal on the line L. Homework Equations L passes through the vectors u = [9; 7] and v = [1; -5] The Attempt at a Solution I found the slope of L from the two vectors: 3/2. I know that to be orthogonal, the vector will have a...

I'm not sure that I understand the vectors \hat{r}, \hat{\theta}, and \hat{\phi} in spherical coordinates correctly. I was looking through this link earlier. I understand that \hat{r} always points radially outward from the origin. That seems to imply to me that any position in space could be...

Homework Statement Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat. Homework Equations r-hat=cos(phi)x-hat+sin(phi)y-hat phi-hat=cos(phi)y-hat-sin(phi)x-hat, The Attempt at a Solution I have been working on this for a really long time, and I keep getting a...

I have a worksheet that due to missing the lecture I'm now stuck on. You are given a cartesian vector and told find the polar unit vecors and hence express the original vector as a linear combination of the polar unit vectors just found. I've searched resources online but feel that there is...

Let \vec{A} represent any nonzero vector. Why is \frac{\vec{A}}{A} a unit vector and what is its direction? If θ is the angle that \vec{A} makes with the positive x-axis, explain why \frac{\vec{A}}{A}\cdot\hat{i} is called the direction cosine for that axis. I am self-studying and this...

Homework Statement r1=(0m) r2=(2000i + 1000j)m v1=(200j)m/s v2=(200i-100j)m/s Homework Equations tantheta=vy/vx v2^2=v1^2+2ax v2=v1+at x2=x1+v1t+1/2at^2 The Attempt at a Solution Thank you for any help

The start of a new school year in Ap physics C, and our favorite engineering professors causing students distress! Maybe the champions of the textbook can help me out... = ) Homework Statement 1. Two vectors are given by a = 4i hat - 3j hat + k hat b = -i hat +j hat + 4k hat. Find a) a + b...

When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it...

So I am given the vector 1...but I need to find vector 2 and 3, in order to find U=(v1, v2, v3), and U is a unitary matrix. Vector 1 is: (1/2+1/2i 1/2 1/2i)^T The example from my notes shows me how to find U, but I am also given a matrix S to start with... Any clue where to start?

Homework Statement Find two unit vectors that are normal to the plane determined by the points A(0,-2,1), B(1,-1,-2), and C(-1,1,0) I found the cross-product of the two position vectors then i got 8i+4j+4k then i divided that by the magnitude to get the unit vector but how do i find the other...

Hello, Could someone please review my work and see if it is correct. Thanks :smile: Homework Statement Find two unit vectors orthogonal to both given vectors. i + j + k, 3i + k Homework Equations The Attempt at a Solution So I used cross product and got A x B= i+2j-3k...

Homework Statement What are the x- and y-components of the polar unit vectors \hat{r} and \hat{\theta} when a. \theta = 180° b. \theta = 45° c. \theta = 215° Homework Equations The Attempt at a Solution Please check if I'm correct, i'll just show my answer for a since the process is...

Homework Statement if \vec{e_{1}} = 5\hat{i} - 3\hat{j} + 2\hat{k} what is the unit vector \hat{e_{1}} Homework Equations The Attempt at a Solution here is my answer,, please confirm if I'm correct. |\hat{e_{1}}| = \sqrt{\vec{e_{1}} . \vec{e_{1}}} |\hat{e_{1}}| =...

Homework Statement The Hyperbolic coordinate system is given by: u=2xy and v=x^2 - y^2 a.) Find the unit vectors u and v in terms of u,v,x(hat),y(hat) b.)Find the time derivatives of u(hat) and v(hat), your answers will have du/dt and dv/dt in them Homework Equations None really...

If I have a negative quantity pointing in the positive z direction, is that the same as a positive quantity pointing in the negative z direction? e.g. does -A\hat{z}=A\hat{-z}?

Hello, I am trying to find the angle between two unit vectors but I was wondering what I am supposed to do when the dot product is greater than 1 or less than -1. For example -0.0288067i + -0.989524j + -0.141463k 0.169194i + -0.0644865j + -0.983471k

can i get some help in how i can convert from cartesian to cylindrical and spherical unit vectors and vice versa ? thank you

Homework Statement Does anyone know what d(r-hat)/d(theta) in Cylindrical coordinates is? Homework Equations The Attempt at a Solution I'm pretty sure its -(theta-hat) but I'm not sure, any help? Thanks so much

Homework Statement In cylindrical coordinates: what is d(theta-hat)/d(theta)? Homework Equations The Attempt at a Solution I'm fairly certain it is -rho... without a direction? or is it -rho*theta-hat? Thanks in advance!

Homework Statement A particle moving in xy plane has velocity components in x and y directions Dx/dt = b1+c1t and dy/dt = b2+c2t A) integrate above equations to give displacement components x and y as functions of time B) write the velocity (v) of the particle at time t in terms of...

Hello. :smile: I understand most of the work involved with these types of questions, but there is one point in an example I'm following that I don't understand. Homework Statement Evaluate: I = \int{(z^2)}dS over the positive quadrant of a sphere, where (x,y > 0). Homework...

Homework Statement Let A be an arbitrary vector and let n be a unit vector in some fixed direction. Show that A=(A.n).n+(A*n)*n Homework Equations The Attempt at a Solution I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

When you are modelling elements like tubes, the local x-axis is defined along the tubes length. If a unit vector for the z-axis is not applied, modelling softwares defaults to a coordinate system where the local zx-plane is parallel with the global zx-plane. I'm not sure what that means...

Homework Statement a particle with charge -2.00 C initially moves at v = 1.00 i^hat + 7.00 j^hat. If it encounters a magnetic field B = 60.00 k^hat T, find the force on the particle Homework Equations F = Q (v x B) The Attempt at a Solution I set up a matrix to find the cross...

Three unit vectors v1 v2 and v3 are in R^n. We are told that v1 dot v2= v1 dot v3=1/2. What are the possible values of v2 dot v3. What could the angle be between the vectors v2 and v3 give example for the cases in R^2 and R^3. costheta = (x dot y)/((magnitude of x)(magnitude of y) I...

Here's the problem I've been having difficulty with: Find a vector with a magnitude of 1.00 that bisects the angle between the vectors 5.00i + 11.0j and 2.00i − 1.00j. Give your answer in rectangular coordinates. Someone else had posted this same question before, but the answer that was...

Homework Statement An electric charge e which moves through a material of permeability μ with a velocity v, produces a magnetic field β at a point r given by: β= ((μ*e)/(4*∏))*((v*ru)/(|r|)2) where ru is a unit vector in the direction of r. Find β if v=4i+3j+3k and r=4i+7j+5k. Take...

Can polar co-ordinate system only be defined in a "background" Cartesian co-ordinate system? What I'm confused about is this: the definition of the polar unit vectors or the polar basis is in terms of the parameter theta. Now, before we go about defining our basis we need to define this theta...

Find a vector with magnitude of 1.00 that bisects the angle between the vectors 5.00i + 11.0j and 2.00i - 1.00j. Give your answer in rectangular coordinates. I'm not going to lie, I am terrible at physics and I had no idea how to solve this question, so I asked someone for help. I came out...

greetings in a scalar gradient why does the unit vector has appeared?scalar gradient only represent the change in that scalar quantity along x,y and z axis.then why unit vector along x, y and z comes in picture? advanced thanks.

Where could I find a webpage or guide on how to write unit vectors in terms of sin and cos? I looked through my textbook and tried searching google, but I can't find anything...I must be using the wrong terminology. edit: Delete me! I had one of those epiphany moments and figured it out...

How to explain unit vector visually?

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before. The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the...

The question is: The total force exerted on the top of the mast B by the sail boats forestay AB and backstay BC is 180i-820j (N). What are the magnitudes of the forces exerted at B by the cables AB and AC? I need some serious help with this question. Any help.

I need certain stopping criterion for approximating one unit vector with another. In case there is a perfect match (after a number of iterations), the dot product of the vectors is 1. I need to know (and have a reasoning for) whether in any other case the dot product of the original unit vector...

Prove that if a(t) is a unit vector whose components are functions of t, then the vector b(t) = da(t)/dt is perpendicular to a(t) here i have the parameters that make a(t) a unit vector: 1 = f(t)^2 + g(t)^2 i know of the example sinxi + cosxj = a(t) but that is the only one i can get to work. I...

Homework Statement A golfer takes three putts to get the ball into the hole of a level putting green. The first putt displaces the ball 2.5 m North, the second 4.8 m South-East and the third 5.7 m South-West. Express each of these three displacements in unit vector notation where i is a...

Homework Statement http://img22.imageshack.us/img22/1254/10031833.jpg Homework Equations The Attempt at a Solution My attempt was based on the idea that both triangles formed by the vector components (x component, y component, and the hypotenuse which is the magnitude of the...

If \vec{OA} is the unit vector l_1i+m_1j+n_1k and \vec{OB} is the unit vector l_2i+m_2j+n_2k, by using the cosine formula in triangle OAB find the angle between \vec{OA} &\vec{OB}.. I have tried expressing them as direction cosines , but none of that is working..can anyone point me in the...

A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?

Why are rectangular unit vectors constant in time whereas those of a polar coordinate or spherical coordinate system aren't?

Homework Statement Find all unit vectors in the plane determined by u= (3, 0, 1) and v=(1, -1, 1) that are perpendicular to the vector w= (1, 2, 0). Homework Equations The Attempt at a Solution I'm basically having trouble with the concept and visualizing the problem. Well first I...