Vectors Definition and 1000 Threads

Homework Statement Please see the attached picture Homework Equations Reduced echelon form of the column matrix The Attempt at a Solution I can solve for the first part to find which ones are the bases in ##\mathbb{R}^3## by determining whether in the echelon form, there is a pivot in each...

Because on the book it is said that little angles are vectors but my question is: Are they vectors at all or they are scalar and we assign them a direction by multiplying them by a versor? The same for angular velocity, is it a vector at all or we made it a vector for making the right hand rule...

Homework Statement The truck is to be towed using two ropes. If the resultant force is to be 950 N, directed along the positive x axis, determine the magnitudes of forces FA and FB acting on each rope and the angle q of FB so that the magnitude of FB is a minimum. FA acts at 20° from the x-axis...

I would appreciate any help with this questions because I truly horrid at geometry questions. I've only done (i) to which I've found the answer to be (E). I can't do from from part (ii) on.

Homework Statement Given points of a triangle: A(4,1,-2),B(2,0,0),C(-2,3,-5). Line p contains point B, is orthogonal to \overline{AC}, and is coplanar with ABC. Intersection of p and \overline{AC} is the point B_1. Find vector \overrightarrow{B_1B}. Homework Equations -Vector projection - Dot...

What happens to a mechanical force's real original direction i.e. when we divide it into components of basis vectors, which in turn change as per problem at hand (like gravity components at inclined plane ), how we arrive at correct physics by taking two/three arbitrary directions of our choice...

Hey could anyone please explain how you go about drawing a reciprocal lattice? For example a 2d rectangular lattice to it's reciprocal form? Also... I don't know if this is correct but if you have a 2d rectangular lattice with lattice vectors L=n1a1 + n2a2 would the reciprocal lattice vectors...

Homework Statement I have to find the equation of the line by using any vector a and b in a way that the line fits the triangle generated by vector addition. If you don't understand my statement, look at my attached file. You will understand what I mean by triangle. Is my solution right...

Homework Statement What would be the opposite direction of [E 20 degrees N}? Homework Equations No real equation The Attempt at a Solution Is the opposite direction [S 20 degrees W]?

Homework Statement The ellipse is given as (x^2/a^2) + (y^2/b^2)=1 I´m meant to calculate a tangential vector, a normal vector and find an equation for the tangent using a random point (x0,y0). I´m meant to do this in 2 ways: firstly by using the parametrization x(t)=a*cos(t) and...

haruspex submitted a new PF Insights post Frequently Made Errors in Vectors - Elementary Use Continue reading the Original PF Insights Post.

Homework Statement If magnitude (absolute value) of vectors ( A + B ) ^2 = A^2 + B^2 then: a) A and B must be parallel and in the same direction b) A and B must be parallel and in opposite directions c) it must be true that either A or B is zero d) the angle between A and B must be 60...

I am reading John M. Lee's book: Introduction to Smooth Manifolds ... I am focused on Chapter 3: Tangent Vectors ... I need some help in fully understanding Lee's conversation on computations with tangent vectors and pushforwards ... in particular I need clarification on the nature of the...

Mod note: Moved from a technical section, so missing the homework template. Hi, I'm struggling to understand this problem. I would normal just wait for class but I'm away traveling for work. The question is as follows. A man has a boat that can travel at 15.0 m/s relative to the water. He...

I'm given the example that the space $\mathbb{R}^2$ is spanned by each of the following set of vectors: $$\left\{i, j\right\}$$, $$\left\{i, j, i+j\right\}$$, and $$\left\{0, i, -i, -j, i+j\right\}$$. However, it's not obvious to me how. Let $i = (s, t)$ and $j= (u, v)$ then $\left\{i...

Homework Statement A ball rolls with a velocity of 14 mm/s [W] on a board that is being pulled [E 60o N] at 20.0 mm/s. What is the velocity of the ball relative to the floor? b = ball x = board f = floor Homework Equations V_bf = V_bx + V_xf The Attempt at a Solution I tried to work through...

Homework Statement A plane went 300m/s 35° south of west then 230m/s 20° east of north. What is the magnitude and direction of the 65kg pilot during the 12s turn? Homework Equations Kinematics. Vf = Vi + at, d = ViT + 0.5at^2, Vf^2 = Vi^2 + 2ad The Attempt at a Solution This was a question...

I am trying to show that if (C^ab)(A_a)(B_b) is a scalar for arbitrary vectors A_a and B_b then C^ab is a tensor. I want to take the product of the two vectors then use the quotient rule to show that C^ab must then be a tensor. This lead to the question of whether or a not the product of two...

Hello guys, I have a vectors word problem and I found 2 different ways to solve the same problem but I'm getting different answers. Apparently, both answers are correct since I've looked for the answer online and I found both answers from different sources, so I'm really confused now...

So like the title says, I'm new to Matlab. I took a programming class on Fortran last year before my college changed the requirement so programming is not new to me all together. For a few of my classes we are allowed to use programs such as Matlab and Maple to help us solve problems. Most of...

Homework Statement Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle. 1) What is his current location using a km coordinate...

I want to find basis for a+ax^2+bx^4 belong to p4. I am getting the following result is it right? =>a(1+x^2) + b(x^4) => basis ={1+x^2, x^4} Is that right ? Please help me any help is appreciated.

Homework Statement A space probe has two engines. Each generates the same amount of force when fired, and the directions of these forces can be independently adjusted. When the engines are fired simultaneously and each applies its force in the same direction, the probe, starting from rest...

Homework Statement A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0° west of south (Fig. P3.21). Starting at the same initial point, an expert golfer could make the hole in...

Homework Statement Show that ##||x||_1\geq ||x||_2## 2. Homework Equations ##||x||_1 = \sum_{i=1}^n |x_i|## ##||x||_2 = (\sum_{i=1}^n |x_i|^2)^.5## The Attempt at a Solution I am having a hard time with this, because the question just seems so trivial, that I don't even know how to prove...

If I ever say anything incorrect, please promptly correct me! The state of a system in classical mechanics is specified by point in phase space, the point giving us the position and velocity at a given instance. Could we rephrase it by saying a vector in phase space specifies the system? If...

Homework Statement The point charges in the figure have the following values: q1=+2.1μC, q2=+6.3μC, q3=−0.89μC. Suppose that the magnitude of the net electrostatic force exerted on the point charge q2 in the figure is 0.57 N . Find the distance d and the direction (angle) of the net force...

Here is the problem verbatim: The polar and azimuthal angles of a vector are Θ1 and Φ1. The polar and azimuthal angles of a second vector are Θ2 and Φ2. Show that the angle ϒ between the two vectors satisfies the relation: cos ϒ = cosΘ1*cos Θ2+sinΘ1*sinΘ2*cos(Φ1-Φ2) Hint: write out the...

Homework Statement Calculate ##(\vec a \cdot \vec \sigma)^2##, ##(\vec a \cdot \vec \sigma)^3##, and ##(\vec a \cdot \vec \sigma)^4##, where ##\vec a## is a 3D-vector and ##\vec \sigma## is a 3D-vector formed from the ##\sigma_i## vectors. Homework Equations $$\sigma_1 = \begin{bmatrix} 0 &...

Hi There are so many different kinds of probability distributions regarding a uniform distribution of points on the surface or inside a hypersphere in 2D and 3D and it's hard to see the big picture or any pattern between them. I'm confused and exhausted :) The overall fuzzy plan is to go from...

Homework Statement 3 m/s [E] - 5 m/s [N] Homework Equations I don't know how to solve this- is this done algebraically or another way? The Attempt at a Solution I have no clue. Would this be different if the directions were not like this--- 3 m/s 50° east - 5m/s 67° North. I have no idea how...

Homework Statement Given the initial velocity of 6m/s[North] and the final velocity of 3m/s[East], how would you find the change in velocity? Homework Equations Change in velocity= final velocity- inital velocity The Attempt at a Solution [/B] I don't know how to do this. I know that if the...

I want ask another basic question related to this paper - http://www.tandfonline.com/doi/pdf/10.1080/16742834.2011.11446922 If I have basis vectors for a curvilinear coordinate system(Euclidean space) that are completely orthogonal to each other(basis vectors will change from point to point)...

Homework Statement Show that vector C = (BA + AB) / (A + B) is an angle bisector of A and B. Where vectors are represented by bold font, and magnitudes are regular font. Homework Equations A ⋅ C = A C cos(θ) ⇒ cos(θ) = (A ⋅ C) / (A C) B ⋅ C = B C cos(θ) ⇒ cos(θ) = (B ⋅ C) / (B C)The...

Homework Statement True or false. If v1... v4 are linearly independent vectors in 4D space, then {v1,v2,v3} is also linearly independent. There's a hint: Think about (c for different constant) cv1+cv2+cv3+0*v4=0 I know that linear independence means there's only the trivial solution... which...

Suppose you have a set of vectors v1 v2 v3, etc. However large they are, suppose they span some area, which I think is typically represented by Span {v1, v2, v3} But I mean, if you're given these vectors, is there anything wrong with rearranging them? Because there's a theorem- that "an...

This is my question: What is the largest m such that there exist v1, ... ,vm ∈ ℝn such that for all i and j, if 1 ≤ i < j ≤ m, then ≤ vi⋅vj = 0 I found a couple of solutions online. http://mathoverflow.net/questions/31436/largest-number-of-vectors-with-pairwise-negative-dot-product...

Homework Statement Say I have a vector F something like F = c1(t) x^ + c2(t) y^ were c1 and c2 are some scalar functions of time were you plug in time to into the equation and are given some magnitude. My question seems to be can we define unit vectors/basis vector as a function of time as...

Quick question (a little rusty on this): Why don't unit vectors in Cartesian Coordinates not change with time? For example, suppose \mathbf{r} (t) = x(t) \mathbf{x} + y(t) \mathbf{y} + z(t) \mathbf{z} How exactly do we know that the unit vectors don't change with time? Or in other words...

Homework Statement Homework Equations Rotational Kinematic Equations Kinematic Equations The Attempt at a Solution I honestly have no clue how to get a vector out of this. I thought about an equation: Θ = Θ(initial) + ω(initial)*t + .5αt^2 and how maybe that v = wr could play into this...

Homework Statement A force F = (2ti + 3t^2j) N acts on an object moving in the xy plane. Find the magnitude of change in momentum of the object in time interval t=0 to t=2 (The bold ones are vectors) Homework Equations Ft=change in momentum The Attempt at a Solution magnitude of F = (4t^2 +...

Homework Statement Linearly polarized light in the x direction with wave number ##k_0## travels in the z direction. It enters a medium such that a RHCP component of the wave and a LHCP component each accumulate a phase of ##n_Rk_0z## and ##n_Lk_0z## respectively, where z is the distance...

Homework Statement So my textbook states that F = ma = m(d2r/dt2) can be integrated to give r = r0 + tv0 when F = 0. Homework EquationsThe Attempt at a Solution I've tried rewriting it as F = m(dv/dt) and integrating that to give Ft = mv + c but this is obviously not in the right form. I've...

I am currently studying a course on waves, which has a real ambiguity in the lecture notes. Essentially, I don't know how the professor got from equation \ref{eq:surf_x-y} to equations \ref{eq:vel_u} and \ref{eq:vel_w}. I have tried to work backwards to find a method but am not sure of its...

Homework Statement Homework Equations p.q+p.r The Attempt at a Solution I've expanded p.(q+r) to give p.q+p.r. The magnitude of p is 3, and since ABE is an equilateral triangle, the magnitude of q is also 3, right? So then p.q=9, but the answer scheme states that p.q=4.5. I'm still pretty...

Hi this isn't my homework, but it is taken from a worksheet for a Maths course(trying to refresh my rusty math), so I hope it fits in here. 1. Homework Statement two cylindrical polar vectors with same origin: P(2,55°,3); Q(4,25°,6) units in m Homework Equations a) Express in cartesian...

Hello everyone, I have a very basic question about future-directed vectors. Are they defined as those vectors whose temporal component is positive or strictly positive? I need to check wether a certain system satisfies the null energy condition or not and I was wondering if I am allowed to take...

I have a velocity vector as a function of a latitude and longitude on the surface of a sphere. Let us assume I have a point V(lambda, phi) where V is the velocity. The north pole of this sphere is rotated and I have a new north pole and I have a point V'(lambda, phi) in the new system. I have...

Homework Statement Show that the sum of two future-pointing null vectors is a future-pointing time-like vector, except when the two null vectors have the same direction. Conversely, show that any time-like vector can be expressed as a sum of two null vectors. For a given time-like vector the...

Homework Statement I need to prove the following: a) If ##P^{a}## and ##Q^{a}## are time-like and ##P^{a}Q_{a}>0##, then either both are future-pointing or both are past-pointing. b) If ##U^{a}##, ##V^{a}## and ##W^{a}## are time-like with ##U^{a}V_{a}>0## and ##U^{a}W_{a}>0##, then...