Vectors Definition and 1000 Threads

Actually that's very easy question but I have some difficult to understand the logic behind . So-"The initial velocity of an object (m/s) is Vi=1i+5j+2k. And the final velocity is Vf=3i+5j+7k. What was the change in speed of the object?"X Solution - |Vf|-|Vi| = √(32+52+72)-√(12+52+22) = 3.63...

∴1. Homework Statement Find an equation for the plane that contains the point (1,-1,2) and the line x=t, y=t+1, z=-3+2t? 2. Homework Equations The Attempt at a Solution I don't know what I am doing wrong but everytime I try to do these plane questions my amswer is always the opposite sign of...

Hi. I have this problem with differentiating vectors. Primarily because I have no experience at all (or whatsoever) about differentiating vectors. I am at a total loss here. I even have no idea regarding the difficulty of this (thus the [ I ] prefix). Please help me. How did the two equations...

Homework Statement Sandra needs to deliver 20 cases of celery to the farmers' market directly east across the river, which is 32 meters wide. Her boat can move at 2.5 km/h in still water. The river has a current of 1.2 km/h flowing downstream, which happens to be moving in a southerly...

Homework Statement let \epsilon_1 and \epsilon_2 be unit vectors in R3. Define two complex unit vectors as follows: \epsilon_{\pm} = \frac{1}{\sqrt{2}}(\epsilon_1 \pm i \epsilon_2) verify that epsilon plus minus constitutes a set of complex orthonormal unit vectors. That is, show that...

Homework Statement The thick arrows represent forces exerrted upon the mast Let ## \vec{r_2} = ~~the~~ longer~force~ vector~~## ## \vec{r_1} = ~the ~shorter ~force ~ vector## correspondinly ## \vec{R_2} = cable ~~2## ## \vec{R_1} = cable~~1 ## r_1 is in the same direction as R_1 r_2 is in...

(I am not very sure if this is a high-school level question or a undergraduate level question. Sorry.) Does our normal differentiation rules, like the product rule and quotient rule apply to vectors? Say for example, differentiate ##r \times \dot r## ##r## is radius vector, ##\dot r## is the...

Homework Statement If I had two vectors say ⟨em|f⟩⟨f|em⟩ does this equal |⟨em|f⟩|2? e is a basis and f is some arbitrary function. I ask this because I have a problem which is to show the following: Show that for the Fourier expansion of |f⟩ in terms of Fourier basis vectors |em⟩ is...

Background: I have just started studying vector algebra. I studied that physical quantities like velocity, force, momentum, etc. are vectors (My book addresses them as polar vectors/true vectors) and physical quantities like quantities like angular velocity, torque, angular momentum are also...

Suppose a second rank tensor ##T_{ij}## is given. Can we always express it as the tensor product of two vectors, i.e., ##T_{ij}=A_{i}B_{j}## ? If so, then I have a few more questions: 1. Are those two vectors ##A_i## and ##B_j## unique? 2. How to find out ##A_i## and ##B_j## 3. As ##A_i## and...

Hey y'all, my first thread here, Got a burning question that has been disturbing my serenity. In all derivations of the stress tensor that I've seen they didn't explain it that much, So my question is, why do the traction vectors on each surface are independent? From what I understood, the...

Hi, hopefully a quick question here...how do you calculate the angle between two vectors if the only information you have is the value of their scalar product and the magnitude of their cross product? Thanks! Andy

Homework Statement There are two problems: 1. At the instant the switch is closed determine the direction of the net force exerted by the magnet on the wire segment at the instant that the magnet is in the position shown. Explain. 2b. Suppose the a third wire, carrying another current i0 out...

Hello, I have a question about why I can't determine the angle between two vectors using their cross product. Say there are two vectors in the XY-plane that we want to find the angle between: A = -2.00i + 6.00j B = 2.00i - 3.00j The method to do this would be to work out the scalar product of...

I'm looking at different ways to express the derivative a curve, like circular and tangent/normal components. Is there no such way that let's you express a vector integral in terms of information from the vector you want to integrate?

Hi--I have two vectors ##x=(x_1, x_2, ..., x_n)## and ##y=(y_1, y_2, ..., y_n)##. Now I want them to be multiplied in the following way: for each ##i=1,2,..,n##, I need ##x_i*y_{i-1}-y_n##. Can anyone help me on how to code this in Matlab? BTW, I also want to input the length of the two...

Why is there a need to find unit vector? If we are given a vector we can always find its direction.

Hi, beginner coder here. I have a somewhat solid understanding of both vectors and functions, and have used the two of them many times, but I'm have trouble coding functions that have vectors in their parameters and as their return values. Another thing I'm having trouble with is calling the...

Hello there, get the notion of position vectors for a particle, but why we use it instead of cartisean coordinates XYZ? What info does the vectors tell us that the cartisean coordinates doesn't tell us? So if we say a point has coordinates x=2, y=3, z=5 We say its position vector is r=i 2 +...

In my ignorance, when first learning, I just assumed that one pushed a vector forward to where a form lived and then they ate each other. And I assumed one pulled a form back to where a vector lived (for the same reason). But I see now this is idiotic: for one does the pullback and pushforward...

An orthogonal basis set spanning R4 has four vectors, v1, v2, v3 and v4. If v1 and v2 are [ −1 2 3 0 ] and [−1 1 −1 0 ] find v3 and v4. Please explain this in a very simple way.

Homework Statement [/B] "An airplane is flying on a bearing of 340 degrees at 400mph. A wind is blowing at a bearing of 320 degrees at 30mph. Find ground speed and direction of the plane." Homework Equations vx=vcosϕ vy=vsinϕ The Attempt at a Solution [/B] First, my teacher told us to change...

Hi everyone. What are the components of the 2 Translational Killing Vectors in 2-dimensions, in Polar Coordinates? I've solved the Killing equation using Maple, and the solution was ##\xi_r = 0##, ##\xi_{\theta} = r^2##, but I guess that these are the components for the rotation Killing Vector...

Hello, I apologize in advance for the way this post looks. I am new to this forum and I've never used LaTeX Primer. I noticed that someone has prevoiusly asked the same question, but I still do not understand how to get to the answer. Also, I tried posting an image but I could not; and this...

Homework Statement A gardener pulls a roller of mass 85 kg over a step. The roller has a radius of 0.25 m. The handle is attached to an axle through the centre of the roller at an angle of 45 degrees to the horizontal. Here's a link to the diagram below, it's figure 1 and 2 on question 18...

Hello, Could someone please check my answer to this problem involving vectors. I have a feeling my answers are totally off; especially for B and C. All my work and applicable equations are shown in the pictures below. If my answer is wrong, please provide me with guidelines for solving the...

Homework Statement It's just an example in the textbook. A vector in cylindrical coordinates. A=arAr+aΦAΦ+azAz to be expressed in cartesian coordinates. Start with the Ax component: Ax=A⋅ax=Arar⋅ax+AΦaΦ⋅ax ar⋅ax=cosΦ aΦ⋅ax=-sinΦ Ax=ArcosΦ - AΦsinΦ Looking at a figure of the unit vectors I...

So I know what these are 4 translation : ##\frac{\partial}{\partial_ x^{u}} = \partial_{x^u}## 3 boost: ##z\partial_y - y \partial_z## and similar for ##x,z## and ## y,x## 3 rotation: ##t\partial_x + x\partial_t ## and similar for ##y , z## however I want to do it by solving Killing equation...

Homework Statement Homework EquationsThe Attempt at a Solution the answer given is the same but without the negative sign, I don't understand because the crossproduct of unit vectors when using a Cartesian coordinates of the directions given by the right-hand rule? Is the positive z...

1. A car is traveling 9m/s Northwest. 8 seconds later it has rounded a corner and is now heading North at 15m/s. This was a question from my textbook and was an example question - so they supplied answers. I was able to work through all of it finding everything except the last question. They...

What is the definition of convergence in calculus for vectors?

Hi everyone, Given a vector-valued function ##\vec{A}##, how do I show that: $$\vec{\nabla} \times \left(\frac{\partial \vec{A}}{\partial x}\right) = \frac{\partial}{\partial x}(\vec{\nabla} \times \vec{A})$$ In other words, are the cross product and derivative commutative w/ each other? I...

Hi. I've been thinking about vectors, coordinate systems and all things associated for a long time. I'd like to know if (at least in the context of General Relativity) my interpretation of these subjects is correct. I will try to summarize my thoughts as follows: - We start with a general...

The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I...

When it comes to analytic geometry, I am little confused about the use of vectors. For example, throughout high school, one works in ##\mathbb{R}^2##, and geometric objects such as lines are described using equations relating two variables, the x and y coordinate, such as y = 2x + 1. However...

My textbook states that "The velocity has the same direction as the displacement". I feel this statement is incorrect. Keeping in one dimension, let's say that I move in the +ve direction at velocity v for some time t. My displacement is vt which points in the +ve direction. However I then stop...

So I understand that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω. And I understand that one can pull back the integral of a 1-form over a line to the line integral between the...

Homework Statement In each of the diagrams (please see attached file (I am sorry for the rotated, the original was in normal form but when uploading it, it was somehow rotated)) and the description of each case below, a particle is moving on a smooth surface, so that the reaction force R acting...

Homework Statement A plane flies 413 km east from city A to city B in 49.0 min and then 814 km south from city B to city C in 1.70 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and...

Homework Statement Is it true in three dimensions that any two vectors perpendicular to a third one are parallel to each other? Homework Equations Dot product. The Attempt at a Solution I've come up with two vectors that were orthogonal to a third and found the angle between them using the...

$\tiny{231.12.3.19}$ $\textsf{Given $v=-7i-j$ and $w=-i-7j$}\\$ $\textsf{find the angle between v and w}\\$ $\displaystyle \frac{\left(-7, -1, 0\right)\cdot\left(-1, -7, 0\right)} {\sqrt{50}\cdot \sqrt{50}} =\frac{14}{50}\approx 0.28$ $\arccos(0.28)\approx 73.74^o$ $\textit{not sure if this is...

Homework Statement As part of a longer problem: "Find necessary and sufficient conditions for the point with positionvector r to lie inside, or on, the tetrahedron formed by the vertices 0, a, b and c." Homework Equations I am not sure... vector addtion? The Attempt at a Solution I don't...

Homework Statement [/B] 1. Suppose {v1, . . . , vk} is a linearly independent set of vectors in Rn and suppose A is an m × n matrix such that Nul A = {0}. (a) Prove that {Av1, . . . , Avk} is linearly independent. (b) Suppose that {v1, . . . , vk} is actually a basis for Rn. Under what...

In string theory, if we have NN BCs along ##X^i, i = 1, \ldots, n-1## and DD BCs along ##X^a, a = n, \ldots, 25## then you get, from ##\alpha^{i,a}_{-1}|0,p\rangle ##, ##n## massless vectors and ##24-n## massless scalars. I understand that for the first excited level, ##M^2=0## and so we have...

I am using arpack (the dsdrv1 driver) to iteratively solve the eigenvalue problem Ax = λx I am interested in the first m eigenvectors, and I have very good initial approximations for these vectors, so I would like to use my m starting vectors as an initial guess. However...

$\tiny{s6.12.3.17}\\$ $\textsf{ Find the angle between the vectors $a$ and $b$}\\$ \begin{align} \displaystyle a&=\langle 3,-1,5\rangle &b&=\langle -2,4,3\rangle\\ \\ \cos\left({\theta}\right)&=\frac{(3\cdot -2)+(-1\cdot4)+(5\cdot3)} {|\sqrt{35}|\cdot|\sqrt{29}|}\\ &\approx 0.1569 \\...

$\tiny{s6.12.3.35}\\$ 35. Find the unit vectors that are parallel to the tangent line to the parabola $y = x^2$ at the point $(2,4)$. \begin{align} \displaystyle y'&=2x \end{align} the book answer to this is $\pm\left(i+4j)/\sqrt{17}\right)$ but don't see how they got this?

Hey! :o For the polynomial vector space $\mathbb{R}[x]$ of degree $\leq 3$ we have the following three bases: $$B_1 = \{1 - X^2 + X^3, X - X^2, 1 - X + X^2, 1 - X\} , \\ B_2 = \{1 - X^3, 1 - X^2, 1 - X, 1 + X^2 - X^3\}, \\ B_3 = \{1, X, X^2, X^3\}$$ How can we determine the following...

Hey! :o Let $t\in \mathbb{R}$ and the vectors $$v_1=\begin{pmatrix} 0\\ 1\\ -1\\ 1 \end{pmatrix}, v_2=\begin{pmatrix} t\\ 2\\ 0\\ 1 \end{pmatrix}, v_3=\begin{pmatrix} 2\\ 2\\ 2\\ 0 \end{pmatrix}$$ in $\mathbb{R}^4$. I want to determine a maximal linearly independent subset of $\{v_1...

Homework Statement Given the ## r(t) = ae^{kt}## , ##θ(t)=kt## find the velocity function that is dependent on ##r##. ##v(r)=?## Homework Equations 3. The Attempt at a Solution [/B] My attempt: 1)##r(t) = ae^{kt}## 2)##{\dot r(t)} = ake^{kt}## From the first equation: ##\ln...