Unit vector Definition and 167 Threads

In rectangular corr. 3i+j mean leght in x-direction =3 in y-3direction =1 However, how about in polar coorindate? 3r+1\theta (r and \theta are the unit verctor in polar coor., I don't know how to type it out, I hope you understand.) Dose it mean a line with length 3 from origin and angle...

Homework Statement Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4) Find a unit vector that is perpendicular to triangle PQS Homework Equations Cross and Dot Product The Attempt at a Solution Correct me if I'm doing wrong. I have two solutions that I've thought: 1)What I...

Homework Statement okay i don't have the exact problem in front of me right now but it went something like this: they gave the force, F, which equaled 500 N. for part a they said to express in terms of a magnitude times a unit vector. for part b they wanted the force expressed in orthogonal...

Homework Statement Consider the following vectors: a = (5.0m) i + (2.0m) j b = (-14m) i + (6.0m)j Sum of a+b in unit vector notation? Homework Equations The Attempt at a Solution I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m)...

Hi to everyone. I'm detecting collision between two ellipses. I've got my unit vector, my ellipse center and radius (horizontal and vertical). I want to calculate the point that lies in the ellipse on the direction of the unit vector. See the image attached. Suppose the red arrow is my unit...

Homework Statement Find a unit vector orthogonal to A in the plane B and C if A=2i-j+k B=i+2j+k and C=i+j-2k Homework Equations The Attempt at a Solution Im thinking the solution is to take the cross product of B and C. and that would be the solution??

Homework Statement Question 3 (a)A long metal cylinder of radius a has the z-axis as its axis of symmetry.The cylinder carries a steady current of uniform current density J = Jzez. Derive an expression for the magnetic field at distance r from the axis,where r<a. By resolving the...

Homework Statement Given that a = (-1,16,-1) and b = (-18,-15,-15), find the unit vector which is perpendicular to the plane containing a and b. There are two possible answers. Choose the answer with a positive x component. Homework Equations (a*b) = (a2*b3-a3*b2)i -...

Homework Statement Find a unit vector (a) parallel to and (b) normal to the graph of f(x) at the given point. Then sketch a graph of the vectors and the functions. Function: f(x)=xx Point: (3,9)Homework Equations The Attempt at a Solution...

Find Unit Vector perpendicular to the Surface, x3+zx=1 at the point P=(1,2,-1) I figures that the perpendicular vector would be, N(X)=grad(x3+zx) = (3x2+z, 0, x) N(P)= (3,0,1) Then the unit vector would be, n=N(P)/||N(P)|| n=(3/51/2,0,1/51/2) The answer i get is not the...

Homework Statement Homework Equations Torque is equal to the derivative of angular momentum with respect to time The Attempt at a Solution I took the derivative of each function given in parts a - d and plugged in the value for t to get my answer for the torque. I don't quite...

Homework Statement Find the unit vector e at P=(0,0,1) pointing in the direction along which f(x,y,z)=xz+e-x2+y increases most rapidly. The Attempt at a Solution In order to find the direction where f increases most rapidly, I found the second derivative of f. I don't know how to put the...

Homework Statement Consider the points (x, y) = (0,0) and (100,10). Calculate the unit vector u pointing from the first to second. If each coordinate has an uncertainty of +/-2, calculate the uncertainty in u using propagation of error, but making reasonable approximations based on the values...

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...

Homework Statement See first figure. Homework Equations The Attempt at a Solution See second figure. When I set t = 0 in \vec{r(t)} I get 0\hat{i} +2\hat{j} + 1\hat{k}. I know this is a vector and not a point but it has the same "coordinates" as the point they are asking us...

Given the formula for an ellipse in x and y and centered on the origin, I need a formula for the x and y components of the normal unit vector at any point (x,y) on the ellipse (y>0). My calculus skills are rusty, and I haven't been able to figure this out. Thanks in advance for any help.

Homework Statement For the scalar field f(x, y, z) = x2 − y2 − z find gradf and normal unit vector to a surface f(x, y, z) = 0 at the point (1, 1, 0). Homework Equations The Attempt at a Solution I calculated gradf= 2xi -2yj -k at (1,1,0) this is = 2i -2y -k normal unit...

So I'm trying to find out what the procedure is to convert a cartesian unit vector to a cylindrical unit vector. Any thoughts?

Homework Statement Linear Algebra: For all the unit vectors u=[x,y,z]^T in R^3. Find the one for which the sum x+8y+2z is minimal. (u is a 3 x 1 vector) Homework Equations The Attempt at a Solution I tried working this with the least squares method...it wasn't right. I am...

Given two vectors \vec{A} = - 2.00 \hat{ i } + 3.00 \hat{ j } + 4.00 \hat{k} and \vec{B} = 3.00 \hat{ i } + 1.00 \hat{ j } - 3.00 \hat{k}. Obtain a unit vector perpendicular to these two vectors. Express your answer as a unit vector N_unit in the form N_x, N_y, N_z where the x, y, and z...

I was given the question, If u=ai+2j+4k and v=3i+bj+k, calculate a and b in a textbook from school (revision for a test). Any thoughts?

Homework Statement Given vector v = <3, -4>, find a unit vector u in the direction of vector v. Give your answer for u as u = <a, b> and u = ai + bj Homework Equations none The Attempt at a Solution Would I use y2-y1 and x2-x1?

Homework Statement Find a unit vector which is perpendicular to both of the vectors a = 4i + 2j - 3k and b = 2i - 3j + k c = xi + yj + zk Homework Equations a\botc \longrightarrow a \bullet c The Attempt at a Solution Okay, here's what I've done so far. Take the dot-product of...

Homework Statement A 5.0 μC point charge is located at x = 1.0 m, y = 3.0 m, and a −4.0 μC point charge is located at x = 2.0 m, y = −2.0 m. a) Find the magnitude and direction of the electric field at x = −3.0 m, y = 1.0 m. [5 Marks] b) Find the magnitude and direction of the force on a...

Homework Statement Find the magnitude and direction of A + B for the following vectors. A = -4 i - 1 j, B = 8 i -2 j How do I find the magnitude of A+B, and also the degree clockwise from the +x direction?

Homework Statement Vector A has a magnitude of 9m. find the angles and the vector AHomework Equations u-hat equals the vector u divided by its length cos alpha=Ax divided by A cos Beta=Ay divided by A cos gamma=Az divided by AThe Attempt at a Solution i do not know where to begin because 9...

Unit Vector notation?? The vector position of a particle varies in time according to the expression r = (3.0i +6.0j)m Find expressions for velocity and acceleration as functions of time. I have NO IDEA HOW TO DO THIS.

Homework Statement Find a unit vector that is orthogonal to both i + j and i + k. I know I can solve this using the cross product of the two. But This chapter is about dot product and not cross product. I am not sure how I could go about solving this problem using the properties of...

Homework Statement Exactly 2.9 seconds after a projectile is fired it has the velocity (9.0i +4.5j) m/s. What is the horizontal range of the projectile. Homework Equations The Attempt at a Solution Range = [((9.0i^2 + 4.5j^2)^1/2)^2 x sin2(arctan(4.5/9))]/ 9.8 m/s/s Range =...

Hello, I am calculating Unit vector for non orthogonal Cartesian grid. To calculate Unit Vector I need to project eg. y and x distance of east face of cell on i and j axis resp. I am using following formula- Unit vector= Ue Surface area= Se=sqrt(dx2+dy2) Ue=(dy/se)i-(dx/se)j Can anybody...

What PARALLEL UNIT VECTORS are and Why i got to divide a vector with its value to get a PARALLEL UNIT VECTOR ? This way \hat{a} = \stackrel{\rightarrow}{A} /|\stackrel{\rightarrow}{A} | ? I am sure that the answere would be very easy but i am such a . . . ! Please help!

Homework Statement Use Stokes' theorem to show that \oint\ \hat{t}*ds = 0 Integration is done closed curve C and \hat{t} is a unit tangent vector to the curve C Homework Equations Stokes' theorem \oint F* \hat{t}*ds = \int\int \hat{n}*curl(F)*ds The Attempt at a Solution Ok...

Hello, I am trying to calculate unit vector for velocity (vel= (U*Unit vector)/unit vector). But if I consider calculation by angle change e.g. unit vector= cos(theta) at certain angle velocity becomes infinity. Please inform me how I can take care of this problem. Thanks in advance.

Homework Statement Given the vectors u = (2, 0, 1, -4) v = (2, 3, 0, 1) Find any unit vector orthogonal to both of them Homework Equations I know that two vectors are orthogonal if their dot product is zero... The Attempt at a Solution I don't even know how to begin! I know the unit vector...

Hi, I have a little confusion with vectors. I have memorised the formula so I can apply it, but I don't feel I really understand how it works. One thing that confuses me is this. How does a unit vector exactly show direction. I've memorized and can blindly believe that this is how it is...

Homework Statement http://img245.imageshack.us/img245/2353/87006064.th.jpg I need to find the unit vector in the direction of \vec{F} at the point (1, 2, -2). Homework Equations The Attempt at a Solution well first of all I need to find what F is right, which is gradf.. how can I get...

Hello, I am trying to extract the 3 angles from a unit vector to position a part on a 5 axis milling machine: This machine has 3 linear axes (x,y,z), direct coordinate system It has 2 rotary axes: A turns about the x (called 'tilt') C is carried on the A axis (called 'rotary') See...

the car problem in my text uses the unit vector, and the second one doesn't... how come?

Homework Statement Find a unit vector that is parallel to the vector from )5,1,-3) to (2,1,1) Homework Equations The Attempt at a Solution I will appreciate any HINT for this problem b/c I am totaly confused from the why how the question is stated. Please help.

Ok, so a vector is direction and magnitude, and by finding the unit vector we divide the vector by the length of that vector, |v| does that mean we get the direction of the vector? tanks a bunch

Homework Statement If d1 = 3i - 2j +4k and d2 = -5i + 2j -k, then what is (d1 + d2) . (d1 x 4d2)? Homework Equations c = absin(theta) --> vector product c = abcos(theta) --> scalar product The Attempt at a Solution I looked at a sample problem and they show the distributive law for...

Homework Statement Vector B has x- and y-components 2 and 6, respectively. Compute the component of B that is parallel to A. A is 3i+4j Homework Equations The basic S(A)=B is all I know. The Attempt at a Solution No clue. Was absent yesterday. (Which is why I need help, lol.)

hi! I'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out? The question is: "Find a unit vector with a...

Homework Statement Find a unit vector (a) parallel to and (b) normal to the graph of f(x) at the given point. F(x)= -x^2 + 5 Point= (1,4) Homework Equations no equations really. The Attempt at a Solution Im not exactly sure what find a unit vector to the parallel and to the...

A) Find the unit vector parallel to tan(x) at (Pi/4, 1) B) Find the unit vector normal to tan(x) at (Pi/4, 1) dy/dx tanx = sec2x and sec2x evaluated at x = Pi/4 is 2. So the slope of the parallel line is 2, but how do I then derive the unit vector?

i get that a unit vector is U/modU but how would it be written for example 8i-4j-8k would it be simply (8i-4j-8k)/144?

Homework Statement An electron has an initial velocity with an x component of zero, a y component of 17.2 km/s, a z component 20.7 km/s, and a constant acceleration of 1.95 x 1012 m/s2 in the positive x direction in a region in which uniform electric and magnetic fields are present. If the...

Hi, I have encountered the following problem in my research. As I do not have a strong background in probability theory, I was wondering if anyone here could help me through the following. I would like to know how one makes rigorous the problem of randomly choosing a unit n-dimensional...

x is a unit vector \in \Re^{2}. My textbook states that \frac{x}{||x||}=\frac{1}{||x||}x. What is the point of including \frac{1}{||x||}; why do they divide the vector by its length? Edit: I just looked at a book in Google's database, and from what I understand: e.g. \sqrt{{2^2+2^2+1^2}}=3...

Homework Statement I have trouble solving this following problem: Find a unit vector parallel to this equation 2x-z=4. The answer is supposed to come out as (2x+4z)/(square root of 20). It would be great if someone can show me how to get this answer. Homework Equations The...