Vectors Definition and 1000 Threads

Hi everyone, I've some points I want to make sure of. 1- When converting a "POINT" from a coordinate system to another, I'll just use the derived equation to convert (e.g. (1,2,3) from cartestian to cylindrical: \rho=\sqrt{x^{2}+y^{2}}, \phi=tan^{-1}\frac{y}{x}, z=z 2- When converting an...

Homework Statement Find equation of plan H in R^4 that contains the point P= (2,-1,10,6) and is parallel to plain H2: 4a +4b + 5c-6d = 3 then answer the following questions: A. find normalized normal of plane H which has an angle theta with the normal n= (4,4,5,-6) of H2 such that...

Hi, I wondered whether a well known expression is known that computes the area between two vectors in R^n. By area between two vectors, I mean the area that would be computed by considering the subspace spanned by the two, projecting the entire space to a "parallel plane" and then finally given...

Homework Statement Given that { u1, u2, u3, u4, u5, u6 } are linearly independent vectors in R16, and that w is a vector in R16 such that w ∉ span{ u1, u2, u3, u4, u5, u6 }. a) Is the set { 0, u1, u5 } is linearly independent? b) the set { u1, u2, u3, u4, u5, u6, w } is linearly...

Hello all, Sorry about the crappy title. I'm actually not sure what the call the thing I'm here to ask about, which is why I'm here. In the process of reading about gravitational lensing, I've run across an odd mathematical thing that I just don't know how to handle. When a spherical...

Hi there, I'll come straight out with this, I'm really struggling to understand the conservation of angular momentum. A common example involves someone sitting on a rotating chair holding a rotating wheel. If the wheel is held so that the axis of rotation is vertical then the person...

Homework Statement Hi everyone, my problem is this: Darryl drives his load of tomatoes 14.0 km [E], 6.0 km [N], 12.0 km [ N 15° E], and then 2.0 km [N 65° E]. This takes him 42 minutes. a) Calculate Darryl's distance and displacement. Draw a diagram and show your work. b) Calculate...

Hey, I read that if a four-vector is 'four-orthogonal' to a time-like four vector then it must be space-like. I showed this quite easily. I also read that a space-like vector can be orthogonal to another space-like vector, but can't seem to prove it. I wondered if someone could help me.

Homework Statement Attached, where AC=BC=2R and CD=CE=3R. I need to work out the force the cylinder exerts on the cross section (in order to work out the moment at C). So first I'm trying to work out the free body diagrams for this system. Is it as I've attached? How do I draw the tension...

Left invariant fields on a group G satisfies a lie algebra; say we have an n-dimensional Lie algebra for which the fields ##{X_1, \ldots , X_n}## is a basis. Let these satisfy the algebra ##[X_a, X_b] = c_{ab}^c X_c##. Suppose now that we have a Riemannian manifold with killing vectors...

Homework Statement Proof that (A×B) . (B×A) + (A . B)^2= A^2 . B^2 Homework Equations A×(B×C)=(A . C)B - (A . B)C The Attempt at a Solution Assuming K=(A×B) K . (B×A) + (A . B)^2 = A^2 . B^2 B . (A×K) + (A . B)^2 = A^2 . B^2 B . [A×(A×B)] + (A . B)^2 = A^2 . B^2 B . [(A . B)A...

Homework Statement If two linearly independent vectors are of equal magnitude, prove that their sum is perpendicular to their difference. Homework Equations v1.v2 = 0 The Attempt at a Solution This question doesn't seem that hard but it's really confused me. Help is appreciated...

Homework Statement Prove that (A×B) . [(B×C)×(C×A)]=(A,B,C)^2 where A, B, C are vectors in R3. Homework Equations W×(U×V)=(W . V) U - (W × U) V The Attempt at a Solution Assuming K=(A×B), M=(B×C): K . [M×(C×A)] K . [(M . A) C - (M . C) A] [(M . A)(K . C) - (M . C)(K . A)]...

Homework Statement This is not a homework question,but I will post here anyway. ##\vec{AB}=\left(\begin{matrix} 1 \\ 2 \end{matrix}\right)## ##\vec{CD}=\left(\begin{matrix} 2 \\ 4 \end{matrix}\right)## (a)Prove that ##|\vec{CD}|## is double of ##|\vec{AB}|## (b)Prove that ##\vec{CD}## is...

Why are some quantities vectors while others aren't? For example, we can calculate both current and current density, but why do we only consider current density to be a vector and current a scalar quantity? Is it a purely arbitrary convention or is it something more mathematically fundamental? I...

Sorry - Answered my own question.

I'd like to understand why i cannot seem to be able to define unit polar basis vectors. Let me explain: We have our usual polar coordinates relation to Cartesian: x = r cosθ ; y = r sinθ if I define \hat{e_{r}}, \hat{e_{\vartheta}} as the polar basis vectors, then they should be...

Homework Statement If \underline{v} = a\underline{i} + 2\underline{j} + 3\underline{k} and \underline{w} = 2\underline{i} +b\underline{j} - \underline{k} and |\underline{v}| = |\underline{w}|, find the values of a and b so that \underline{v} and \underline{w} are perpendicular. If v =...

I am a bit confused often when I have to compute cross products in other coordinate systems (non-Cartesian), I can't seem to find any tables for cross products such as "phi X rho." in spherical I think that these unit vectors are considered to be "perpendicular," so would phi X rho just be "+/-...

Hi all, I am having trouble understanding inner products. Specifically, using inner products to find the angle between two vectors. Our lecturer has given an example, as follows; (u,v)= 4u1v1 + u1v2 + u2v1 + u2v2, where u=(1,0) v=(0,1) (u,v)=|u|.|v|cosθ 1=(√4)cosθ θ=∏/3 Surely the...

I want to show a vector in matrix but I didnt uderstand differentes between row matrix and column matrix Let's suppose I have a 2i+3j How I will show this vector in matrix ? I will use a row matrix or column matrix.

Homework Statement Use the componant method to determine the total displacement given by the two vectors shown in each diagram. Homework Equations The Attempt at a Solution I thought I just had to find the third unknown side, and use the pythagorean theorem, but I was...

Homework Statement A cord 7m long has its ends tied to a horizontal board 5m apart. A weight of 50 N is suspended from a ring so that the weight is free to slide along the cord in a vertical plane. A horizontal force pulls the ring to a position such that the cords on either side of the ring...

1. Given info ( with attached photo) The guy wire supporting a 100ft tower has a tension of 550lbs. Use the distance shown in the figure write the component form of the vector F representing the tension of the wire. 2. My attempt at the solution My first assumption was to make a vector using...

Homework Statement The Attempt at a Solution I'm having trouble understanding how r1 = -1.5j and r2= r3 = 0. Can anyone make this a little clearer for me? I've spent quite a while trying to wrap my head around it but to no avail.

How I do for calculate the solid angle formed by 3 vectors like: http://s30.postimg.org/61lpvmi4h/solid.jpg ?

Hi everyone, Just want to know how does the the unit vector become in that form: \vec{n}=\frac{2x\vec{i}+2y\vec{j}}{\sqrt{(2x)^{2}+(2y)^{2}}}=\frac{x \vec{i}+y \vec{j}}{4}

If |vector a+vector b|= |vector a- vector b| show that vector a is perpendicular to vector b. A friend of mine suggested me to square both the sides of the equation. At the end, the result was vector a. vector b=0, from which it could be proved that the vectors are perpendicular. But...

Homework Statement I just want to know how to get from this: ∂ø^/∂ø = -x^cosø - y^sinø to this: = -(r^sinθ+θ^cosθ) Homework Equations All the equations found here in the Spherical Coordinates section: http://en.wikipedia.org/wiki/Unit_vector The Attempt at a Solution I've...

Homework Statement Check if the following set of vectors are linearly dependent or independent: A) V1= \stackrel{1}{1} V2= \stackrel{1}{3} B) V1= \stackrel{\stackrel{1}{2}}{3} V2= \stackrel{\stackrel{2}{1}}{3} C) V1= \stackrel{1}{3} V2= \stackrel{2}{1} V3= \stackrel{-1}{2} Homework...

Hello Everyone! I am working my way through Gilbert Strang's book on linear algebra. I came across a set of solutions to the problems whose solutions are not listed in the book http://www.scribd.com/doc/86849289/1/Problem-Set-1-1-page-8. However, as I was working on the following question: I...

Homework Statement In 3D space a full vector can be represented I. All the following except A. In Cartesian vector form B.As a magnitude times a unit vector C. As a Cartesian vector times a unit vector D. As magnitude with coordinate angles Homework Equations The Attempt at a...

Homework Statement If u know the value of two coordinate angles there is an ulimeted amount of possibility for finding the third coordinate angle A. True B. False Homework Equations The Attempt at a Solution I .not too sure about this one any suggestions would be appreciated I...

Problem 1: Let S1 be a sphere centered at(0, 1, -3) with radius 1 and let S2 be a sphere centered at (3, 5, -9) with radius 2. Find the distance between the two spheres. problem 2: Given three non-zero vectors v1, v2, v3 we say that they are mutually orthogonal when v1 dot v2= 0, v1 dot v3=0 ...

Vectors -- velocity is changing but speed is not... Homework Statement Which pair of vectors represent an object whose velocity is changing but whose speed is NOT changing? Homework Equations The Attempt at a Solution E? V is going left, indicating negative, while acceleration...

Homework Statement I have been doing dot and cross product recently. I get how to calculate everything; however, I am confused about which angle to use when asked to find the angle between two vectors. When you use the cross product, you always end up with 2 answers, for example 120° and...

Homework Statement The dot product for two.parralel pointing.unit.vectors is ? A. 1 B. 0 C. -1 D. Undefined [b]2. Relevant equation The Attempt at a Solutionsince they are unit vectors they have a magnitude of 1,this implies that the dot product is 1,since the angle between...

Homework Statement The dot product of.two vectors is -1which of the following statements is true A. They must be unit vectors pointing in opposite directions. B. They must be unit vectors pointing j. The same direction. C. They must be more than 90( and less than 270 )degrees from each...

Homework Statement Please check my work for the following problem: Find the point(s) where the curve r = <t,t2,-3t> intersects the plane 2x-y+z=-2. 2. The attempt at a solution t + t2 -3t = -2 (t-2)(t+0) = -2 t=0 and t=-2 plugging those values in yields: r(0) =...

Homework Statement In 2-D space, the maximum number of unknown information is... Select one: a. 4 b. 2 c. 3 d. 1 e. 0 Homework Equations The Attempt at a Solution i think the answer is 1 comments would be appreciated

One last question on these topics, I need to choose the WRONG statement, and they all seem correct to me... a) If A is a squared matrix for which \[A^{2}-A=0\] then A=0 or A=i b) If A and B are diagonal matrices, then Ab=BA c) A 4X4 matrix with eigenvalues 1,0,-1,2 is "diagonlizable" d) The...

Represent the below vector relationship geometrically, illustrating two different ways of adding vectors. Vector a - vector b = vector c. I know the above relationship can also be expressed as: Vector a + (-vector b) = vector c. In other words, we flip the direction of vector b and add as...

Hello Everyone, Pardon me if the following is incoherent. From what I understood of what my professor said, he was basically saying that when a vector can be written as a linear combination of some vectors in a span, this means, geometrically, that the vector is in the plane that the span of...

I remember I have read somewhere that contravariant/covariant vectors correspond to polar/axial vectors in physics, respectively. Examples for polar/axial vectors are position, velocity,... and angular momentum, torque,..., respectively. Is this right? Can I prove that, say, any axial...

Homework Statement The vectors r1 and r2 below represent atomic positions in a crystal. r1 = (n1 + n3)ax + (n2 + n3)ay + n3az r2 = (n1 + n3 + 1/2)ax + (n2 + n3 1/2)ay + (n3 + 1/2)az Assume first that the two vectors above correspond to two different types of atom. Find a set of...

See below. I screwed up the edit and the use of tex.

Homework Statement Let x1 = (1, 2, -1, 1), x2 = (-1, -1, -1, -1), x3 = (1, 1, 1, 0), x4 = (-2, -1 -4 -1) Show that x1, x3 and x4 are linearly independent Homework Equations The Attempt at a Solution Now I used the equation: ax1+bx2+cx3+dx4=0 Hence forth the augmented...

Homework Statement So this isn't really a specific homework question, it's more of a general one. What is the difference between ax and i(hat)? I thought they were the same thing. Can someone please explain the difference? Homework Equations The Attempt at a Solution

Homework Statement Given that the primitive basis vectors of a lattice area (a/2)(I+J),(a/2)(j+k), (a/2)(k+i), where I j and k are the usual three unit vectors along Cartesian coordinates, what is the bravais lattice? Homework Equations The Attempt at a Solution So just drawing...

Homework Statement For the following three vectors, what is 2C*(3AxB) A=3i+3j-4k B=-3i+2j+3k C=-6i-8j **All of the capital letters are vectors** Homework Equations The Attempt at a Solution 2A=2(3i+3j-4k) =6i+6j-8k 2AxB=(6i+6j-8k)*(-3i+2j+3k)...