Unit vectors Definition and 140 Threads

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...

Homework Statement My prof gave me a homework assignment and i don't really understand how to do the question. You are give two vectors \vec{A}=(3,1,-3) and\vec{B}=(-2,3,4) a) Find the angle between the two vectors b) Find all the unit vectors (if there are more than one) perpendicular...

When are unit vectors helpful? It seems to me that it is simply a way to rewrite a given vector component, but with an extra, redundant letter (i, j, k). Thanks in advance.

Hi All, I'm currently studying vector projections and the vector dot product. I ran into a problem on the homework I wasn't quite sure how to tackle... Any suggestions?The problem is stated as follows: Determine ||v+w|| if v and w are unit vectors separated by an angle of \frac{\pi}{6}...

Homework Statement Find the tangential and normal unit vectors for an ellipse with major axis of length a in the x-direction and minor axis of length b in the y-direction. Homework Equations For a circle, the unit vectors are defined as \hat{r}=\cos{\theta}\hat{i}+\sin{\theta}\hat{j}...

Does anyone know a good sight that explains, step-by-step, how to derive unit vectors in spherical coordinates? I am at that unfortunate place where I have been looking at it for so long I know the answer from sheer memorization, but don't understand the derivation. From the definitions I am...

Homework Statement http://img4.imageshack.us/img4/4218/divergenceandcurl.jpg The Attempt at a Solution Totally confused on what the question's asking. Wouldn't the divergence of say x_hat be the partial of x_hat over x which is just 0? So every answer would just be 0 or something? Same...

Homework Statement A golf ball is hit off a tee at the edge of a cliff. Its x and y coordinates as functions of time are given by the following expressions. x = (16.0 m/s)t y = (3.30 m/s)t - (4.90 m/s2)t^2 Write a vector expression for the ball's position as a function of time, using...

Homework Statement Well, it's all in the title. I just need to show that Gauss's theorem applies to this fluid flow and have converted all my (x,y,z) components to their respective (r,theta,phi) versions, but I can't remember the spherical counterparts of \hat{x},\hat{y},\hat{z}.

hi, I have this problem I've been stuck with for a long time and i can't figure out what to do. if spherical coordinates are denoted (r,θ,ϕ) and cylindrical coordinates are denoted (ρ,ϕ,z), how do i express the radial unit vector in cylindrical coordinates, e(ρ), in terms of the spherical...

Homework Statement Given a=2i+3j+k, b=i+2j+k, c=-i-j+k, calculate; a)unit vectors b^ and c^ in the directions of b and c respectively. b)the angle between a and c Homework Equations n/a The Attempt at a Solution I don't understand a) at all, but b is just a simple dot product...

I have a question on an assignment that expects the I+J form of a vector but is only giving the direction(cardinal) or angle of the vector. See example below: Homework Statement Unit vectors and are directed east and north, respectively. Calculate the unit vector (in terms of I and J) in...

Homework Statement Suppose that the 1 kg standard body accelerates at 3.40 m/s2 at 155° from the positive direction of the x axis, owing to two forces, one of which is F1 = (2.6 N)i + (4.8 N)j. What is the other force in unit-vector notation and as a magnitude and direction? i-component of the...

Homework Statement Find the unit vectors that are parallel to the tangent line to the curve y=2sinx at the point (\pi/6, 1). Thereafter, find the unit vectors that are perpendicular to the tangent line. Homework Equations The Attempt at a Solution I took the derivative of y=2sinx and...

I've been reading and studying from 'Engineering Mechanics - STATICS 5th edition' by Beford and Fowler and it says that the definition of the unit vector e is that it has a magnitude of 1. Then e.g. V = |V|e Then isn't it just V = |V|? I still find unit vectors pointless/confusing. I need...

Homework Statement http://img361.imageshack.us/img361/7372/87516919cu1.th.jpg Homework Equations \sqrt{}a2+b2 = c w = f s The Attempt at a Solution Pythagoreoms theorem on -8.6 m and -3.0 m to find the distance traveled = 9.11m Pythagoreoms theorem on 34 N and -38 N to find total force = 60...

Homework Statement I know the definition.where could i find detailed information on unit vectors? Homework Equations The Attempt at a Solution

Homework Statement The problem is :''Resolve the cartesian unit vectors into their cylindrical components(using scale factors) The Attempt at a Solution It's simple to do the inverse(resolving cylindricl unit vectors into cartesian components),but I'm having some ''trouble'' with the...

Homework Statement \mathbf{r} = rsin(\theta)cos(\phi) \hat x + rsin(\theta)sin(\phi) \hat x + r cos(\theta) \hat z I am kind of following the description of the process given at http://mathworld.wolfram.com/SphericalCoordinates.html I want to find \hat r and I understand everything except: Why...

Anybody know the history of why something like \mathbf{e}_i is conventionally used for unit vectors (as opposed to u for Unit which is less common). I assume this originates from another language? If so I'm curious what language and what word.

Homework Statement Vector A=(oi +3j), B=(8i-1j), C=(-8i+5j) Find the angle from the positive x-axis of the vector A+B+C Find the magnitude and direction of the vector -A-B+C Homework Equations The Attempt at a Solution I know that the answer is 90, but I'm not sure how to...

Homework Statement Vector A=3i-1j and B=-i-4j Find vector A-B and|vector A-B| Homework Equations The Attempt at a Solution Vector A-B=4i-3j Is the |vector A-B|the magnitude or just the absolute value of the answer? Thank you very much

Homework Statement Electric Charge Problem with Unit Vectors. 20. In Fig. 21-29, particles 1 and 2 of charge q_{1} = q_{2} = +3.40{\textcolor[rgb]{1.00,1.00,1.00}{.}}x{\textcolor[rgb]{1.00,1.00,1.00}{.}}10^{-19}{\textcolor[rgb]{1.00,1.00,1.00}{.}}C are on a y-axis at distance d = 17.0 cm...

What is the benefit of using unit vectors rather than not using them?? I am not seeing the point of them? It seems to me that you can do the same calcs without adding the ihat and jhat. Can someone explain exacly how and why unit vectors make vector calcs easier, or why we need them. Thanks...

Given an orthogonal curvilinear coordinate system (q_{1},q_{2},q_{3}) with standard orthonormal basis vectors (\hat{e}_{1},\hat{e}_{2},\hat{e}_{3}), how would you prove the following?: \frac{\partial \hat{e}_{i}}{\partial q_{j}}= \hat{e}_{j}\frac{1}{h_{i}}\frac{\partial h_{j}}{\partial...

If two vectors v, w are both unit vectors, then v+w and v-w will be orthogonal, but are v+w and v-w also unit vectors? I would say no because the inner product of the two added, and the two subtracted would also have to be orthogonal. <(v+w)+(v-w),(v+w)-(v-w)> = <2v,2w> and <2v,2w> must be...

Homework Statement Find a unit vector in the direction of the given vector. v=5i-2j Homework Equations [[v]]=square root of (V1^2 +V2^2) v/[[v]] The Attempt at a Solution I went 100% simplification.. answer I got was <(5squareroot of 29)/29, (-2squareroot of 29)/29> But the...

Homework Statement Find a unit vector that is (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch. f(x)=x^2 point=(3, 9) Homework Equations None that I'm aware of.The Attempt at a Solution Find parallel or perpendicular lines, planes, vectors, etc. to a given...

Homework Statement The cable AB keeps the 8-kg collar A in place on the smooth bar CD. The y-axis points upward. Determine the distance s from C to the collar A for which the tension in the cable is 150N. location of: B: (0m, 0.5m, 0.15m) C: (0.4m, 0.3m, 0m) D: (0.2m, 0m, 0.25m) collar A's...

I have a problem asking me to find the acceleration of a particle when its v_i = (3.00 \hat{i} -2.00 \hat{j} ) m/s and then 3 seconds later, v = (9.00 \hat{i} + 7.00 \hat{j} ) m/s The big problem here is that my book doesn't say anything whatsoever about getting an acceleration when...

Does anyone know how to derive the spherical unit vectors in the cartesian basis? Or a good link that might show how its done? I would also like to see it done for the cylindrical coordinates. I have tried to do it, especially for the spherical case, but i can only get r-hat. It would be...

What happens if a unit vector is not used in calculating the directional derivative. From when I worked it out the directional derivative is multiplied by a scalar if a unit vector is not used. So I gather that the directional derivative must be calculated by a unit vector. Because it is still...

This is driving me crazy, I just can't see how to do it. I want to express the cartesian unit vectors \hat{x}, \hat{y} and \hat{z} in terms of the spherical unit vectors \hat{r}, \hat{\theta} and \hat{\phi}. I have tried to do something similar in polar coordinates (just to make it a bit simpler...

Does someone want to think along with me? field h(x,y) = x^2 y calculate gradient for this field and draw it for point (1,3): calculate this point: nabla h = (2xy, x^2) = (2*1*3, 1) = (6, 1) But how do I draw this into the field of x^2y? I know I have to draw a vector. Would this...

DJGriffiths, 3rd ed., Prob 1.37: derive the \hat{r}, \hat{\theta}, and \hat{\phi} unit vectors in terms of \hat{x}, \hat{y}, and \hat{z}. I know the formula and how to find them, but derive them?? ...unless this is what is meant? tia, -LD

heres is one problem i did, i photo'd it so i wouldn't have to worry about it... Am I doing it right? any problems can you see :-/ on like the 8th/9th line, I don't think I can do what I did... http://img130.imageshack.us/img130/1332/test076ze.jpg Sooo

Hi please, someone help me with those problems? It's about three dimension space and it is about vectors properties: Find the unit vectors u that are prependicular to both i+2j+k and 3i-4j+2k. the second is: Find two mutually perpendicular unit vectors that are perpendicular to...

There are two vectors (1,0,-1) and (0,1,1) I need to find all the unit vectors x in R3 that make an angle of pi/3 with each of the vectors above. Can someone please help with this problem?

I got the answer to this question but I don't quite understand why its like that...The question is: Find two unit vectors that are parallel to the xy plane and perpendicular to the vector [1,-2,2]