Vectors Definition and 1000 Threads

<Moderator's note: User has been warned not to remove the template, and upload images instead of linking to an external site.> I'm very lost here, I don't know where to begin. My instructor is little help, the notes he gives are not even useful, and I cannot find anything in the book.We were...

Homework Statement A child is flying a large kite of mass 6.8 kg on a windy day. At the moment shown the tension from the string on the kite has a magnitude of 17.0 N and makes an angle of = 32.6° from the vertical, and the acceleration of the kite has a magnitude of ak = 7.72 m/s2 and makes...

Homework Statement In order to solve a question, I need to find the minimum and maximum resultant of three vectors, their magnitudes are given to me. Homework Equations Magnitude of vector A = 1 Magnitude of vector B = 3 Magnitude of vector A = 5 The Attempt at a Solution The maximum part was...

Homework Statement Homework Equations [/B] The two equations in the image, as well as (maybe) standard vector operations like dot product, cross product. The Attempt at a Solution [/B] So, I've tried to do what my instructor suggested and put everything in terms of Earth (Using RE and TE...

Solved (sorry i tried again and realized my E-values were wrong) 1. Homework Statement Homework Equations Find Eigen Values and then what? The Attempt at a Solution I got eigen values as 3 and -3. Now how to proceed? I got Eigen Vector as: 1, 1 for eigen value of 3 and eigen vector as 8, 2...

Hello everyone! I was given the following three questions in my homework, and I had a lot of trouble with them, so I was hoping someone could look them over! If you could just check out my pictures and say "yeah its awesome!" or "nope... [insert helpful answer here]" that would be GREAT. Thanks...

Homework Statement Hello, I havre problem here relevant to an image I will attach. ''A cricket ball hit by a batsman moves with a speed of 6m/s along a straight line path PQRS, as shown in the diagram. When the ball is at R, a fieldsman starts to run in a straight line from T with a speed of...

I currently styding applications of Lie groups and algebras in quantum mechanics. U^{\dagger}(R)V_{\alpha}U(R)=\sum_{\beta}R_{\alpha \beta}V_{\beta} Where ##U(R)## represents rotation. Letter ##U## is used because it is unitary transformation and ##R_{\alpha \beta}## matrix elements of matrix...

It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)## $$P: y_{i} \rightarrow -y_{i}$$ where ##i=1,2,3## But what about vectors in Minkowski space? Is it true that $$P: y_{\mu} \rightarrow -y_{\mu}$$ where ##\mu=0,1,2,3##. If yes how...

Hi I am studying force components on a inclined plane. I understand the concept of breaking vectors into X , Y Components relative to the horizontal plane however what I can't seem to make sense of is how the ratios of a triangle and the main input force being the hypotenuse of the triangle...

Homework Statement A 0.5 kg block of ice is sliding by you on a very slippery floor at 2.5 m/s. As it goes by, you give it a kick perpendicular to its path. Your foot is in contact with the ice block for 0.0035 seconds. The block eventually slides at an angle of 24 degrees from its original...

Hello, I can't seem to arrive at a result that my book states using Jones vectors for circular polarization. My book says that the unit jones vector for right circular polarization is $$ \begin{bmatrix} 1 \\ -i \end{bmatrix} $$ However when I apply this jones vector to an arbitrary electric...

Homework Statement (whole question/answer on IMG file also a scanned version in case) Hello, this question is from my notes and I couldn't figure out the graphing part of it. We're supposed to use limits and see what happens to the equations as x goes to infinity and zero. My question (as you...

Homework Statement The water in the river moves southwest (45 degrees south of west) at 4 mi/h. If a motorboat is traveling due east at 15 mi/h relative to the shore, determine the speed of the boat and its heading relative to the moving water. Homework Equations Vector summation The Attempt...

Homework Statement https://i.imgur.com/UtLzb34.png Homework Equations the law of cosinus The Attempt at a Solution I have not been available to scan my work, but I'm kinda stuck at the beginning. And our teacher have not show us this kind of physics yet. Thanks.

Homework Statement With respect to a given Cartesian coordinate system S , a vector A has components Ax= 5 , Ay= −3 , Az = 0 . Consider a second coordinate system S′ such that the (x′, y′) x y z coordinate axes in S′ are rotated by an angle θ = 60 degrees with respect to the (x, y) coordinate...

Hi, I just have a question relative to matrices, mostly. Is the reason there are 4 values in a matrix because there are (at least in basic terms) 3 dimensions of space and one of time? Like it seems kind of obvious, but for some weird reason in school they never state it explicitly in those...

I don't know whether my question is write or not. Is there any way to obtain the covariant component of the same vector $$\vec{V}$$? or is it just the components when written in terms of spherical coordinate unit vectors?

1. The metric ##g_{\mu \nu}## of spacetime shall be constructed from tensor products of vectors (relevant are the unit vectors in the respective directions). One such vector shall be called ##A##. Homework Equations ##g_{\mu \nu} = \lambda \frac{A_\mu A_\nu}{g^{\alpha \beta} A_\alpha A_\beta}...

Homework Statement In an attempt to escape a desert island, a castaway builds a raft and sets out to sea. The wind shifts a great deal during the day and he is blown along the following directions: 2.50 km and 45.0° north of west, then 4.70 km and 60.0° south of east, then 1.30 km and 25.0°...

Homework Statement At noon two boats P and Q have a position vector (i+7j)km and (3i+8j)km respectively to the origin O. i and j are unit vectors in direction to East and north respectively P is moving south east at 5√2 km/h and Q is moving at a constant velocity of (6i+5j) km/h At time t after...

My question is perhaps as much about the philosophy of math as it is about the specific tools of math: is perpendicularity and rotation integral and fundamental to the concept of multiplication - in all number spaces? As I understand it, the product of complex numbers x = (a, ib) and y = (c...

Hey! :o We have the matrices $E_{k\ell}\in \mathbb{R}^{2\times 2}$ with $1$ iin the position $(k,\ell)$ and $0$ in the other positions and \begin{equation*}\sigma_0=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}, \ \sigma_1=\begin{pmatrix}0&1\\ 1&0\end{pmatrix}, \ \sigma_2=\begin{pmatrix}0&-i\\...

By requiring the inner product in two points ##x## and ##x'## having metrics ##g## and ##g'## to be invariant, i.e. ##g'(x') = g(x)##, one is lead to the Killing equation. Does general relativity forbiddes spaces where the Killing equation cannot be satisfied? It seems obvious that we want...

\tiny{243.12.5.21} $\textsf{Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.}$ $$\textit{$3x+10y+7z=9$ and $7x+ 2y + 9z = 3$}$$ \begin{align*}\displaystyle u&=3x+10y+7z=9\\ v&=7x+2y+9z=3\\ u \cdot...

Homework Statement Write a BinaryTree Class using these specifications: A Class Node represents a standard node of the tree with fields and a constructor like given below: int start, end; const Complex* value; //I will provide more information about Complex later because that was the...

Homework Statement Given the six vectors below: 1. Find the largest number of linearly independent vectors among these. Be sure to carefully describe how you would go about doing so before you start the computation. 2 .Let the 6 vectors form the columns of a matrix A. Find the dimension of...

$\tiny{243.13.0113}$ $\textsf{The vector $r(t)$ is the position vector of a particle at time $t$.}]$ $\textsf{Find the angle between the velocity and the acceleration vectors at time $t=0$}\\$ \begin{align*} \displaystyle...

Homework Statement Vectors A and B are in the xy plane and their scalar product is 20.0 units. If Amakes a 27.4° angle with the x-axis and has magnitude A=12.0 units and B has magnitude B= 24.0 units, what can you say about the direction of B? Answer: 113.4° and 301.4°The Attempt at a Solution...

Homework Statement I’m working on a problem that requires adding 3 vectors . And while I was following the book, it said to find the angle to divide the y over the x components of the resistant , and showed the angle to be -1.25 but then follow d to change to -51 . How did it change ? The book...

I am trying to figure how to get 1. from 2. and vice versa where the e's are bases for the vector space and θ's are bases for the dual vector space. 1. T = Tμνσρ(eμ ⊗ eν ⊗ θσ ⊗ θρ) 2. Tμνσρ = T(θμ,θν,eσ,eρ) My attempt is as follows: 2. into 1. gives T = T(θμ,θν,eσ,eρ)(eμ ⊗ eν ⊗ θσ ⊗ θρ)...

Hello Folks, I have two points on Earth at each end of a great circle path, for which I know the length in km and direction in degrees True. Also I have the RA and DEC of an object in space as seen from one of the previous points. The RA and DEC come from the setting circles of a telescope...

A child is in danger of drowning in the river. The river has a current of 2.5 km/hr . The child is 0.6 km from the shore. A rescue boat with speed 20.0 km/hr (with respect to the water) ,located 0.8km downstream, sets off from the shore. What would be the optimum angle (shore -> boat ) to reach...

Homework Statement Astone is thrown horizontally with an initial velocity of 5 metres per second. What is the magntude and direction of its velocity 0.2s later? Take the acceleration of free fall to be 9.8 metres per second squared and ignore friction. Homework EquationsThe Attempt at a...

Mentor note: Moved from Intro Physics, as this is more of a mathematics question Homework Statement With respect to a prescribed basis... |e 1> |e 2> ...|e n> Any given vector |a> = a1|e1> +a2|e2>+...+a n|e n>, Is uniquely represented by the (order) n-ruble of its components. |a> <--->(...

Homework Statement (i) Reduce the system to echelon form C|d (ii) For k = -12, what are the ranks of C and C|d? Find the solution in vector form if the system is consistent. (iii) Repeat part (b) above for k = −18 Homework Equations Gaussian elimination I used here...

Homework Statement Given the following matrix: I need to determine the conditions for b1, b2, and b3 to make the system consistent. In addition, I need to check if the system is consistent when: a) b1 = 1, b2 = 1, b3 = 3 b) b1 = 1, b2 = 0., b3 = -1 c) b1 = 1, b2 = 2, b3 = 3 Homework...

Homework Statement Prove that in the elastic collision of two objects of identical mass, with one being a target initially at rest, the angle between their final velocity vectors is always 90 degrees. Homework Equations m1v1+m2v2 = m1v1'+m2v2' 1/2m1v1^2 +1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2...

Homework Statement Homework EquationsThe Attempt at a Solution it seems like because theta 2 is independent, therefor, you can solve theta 3 by just using one equation from the system of equation? on a previous problem where its a 4 bar mechanism( which it didn't specify that theta 2 is...

Homework Statement Homework EquationsThe Attempt at a Solution since they are in complex vector form, its missing a " j " on the sin() part, correct?

I'm trying to figure out something regarding the span of a set of vectors. Say we have a set of vectors ##V=\{v_1, v_2, ... v_k\}## in ℝn. If k < n then the set does not span ℝn. Why is this? Are there vectors in ℝn that aren't combinations of the vectors in ##V##?

Homework Statement Three small, identical 0.70-kg pucks are attached to identical 0.50-m strings, tied together at a common center as shown in (Figure 1) . Pucks are whirled in circular motion at angular speed 3.0 s-1 What is the magnitude of the angular momentum of the system about the...

Homework Statement Coupled Harmonic Oscillators. In this series of exercises you are asked to generalize the material on harmonic oscillators in Section 6.2 to the case where the oscillators are coupled. Suppose there are two masses m1 and m2 attached to springs and walls as shown in Figure...

If I have three velocities and am asked to rank them from least to greatest and they are -10 m/s, 3 m/s and 1 m/s I thought it would be 1 m/s, 3 m/s, and -10 m/s. However, someone told me that because -10 was negative, it would technically be the smallest. I found this strange. Who is right...

Homework Statement (a) Consider the line integral I = The integral of Fdr along the curve C i) Suppose that the length of the path C is L. What is the value of I if the vector field F is normal to C at every point of C? ii) What is the value of I if the vector field F is is a unit vector...

Homework Statement For this assignment, I am given sets of forces and asked to solve for the force(s) needed to cancel them out. For this case, I am asked to solve for the missing parts of vectors A, B and C. I was only given vector C's Mass and Direction to start with, but I managed to get all...

How do I express ex,ey,ez in terms er,eθ,eZ? r=(x^2+y^2)^1/2,θ=arctan(y/x),Z=z A(r,θ,z) ∂A/∂x=x/(x^2+y^2)^1/2er+(-y)/(x^2+y^2)eθ=cosθer-(sinθ/r)eθ ex=(∂A/∂x)/|∂A/∂x| I should get ex as cosθer-sinθeθ, but I don't get ex correctly. am i doing this wrong?

Homework Statement For this assignment, I am given sets of forces and asked to solve for the force(s) needed to cancel them out. For this case, I am asked to solve for the last vector, which is vector D. I've successfully found its x and y component, magnitude, and mass (kg). I've also checked...

Homework Statement Bob has a helicopter and from the launch pad he flies the following path. First he travels from the launch pad a distance of 17 kilometers at heading of 63 degrees East of South. Then he flies 45 kilometers heading 73 degrees West of North. After this he flies 34 kilometers...

Homework Statement Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)? Justify your answer algebraically. Homework Equations (x,y,z) = (x0,y0,z0) +s(a1.a2,b3) + t(b1,b2,b3) The Attempt at a Solution...