Vectors Definition and 1000 Threads

Homework Statement Find P-Q (P=11.5 kN, Q=12.5kN) Homework Equations x-component = cos(angle)*force y-component = sin(angle)*force Pythagorean Theorem (to find resultant magnitude): c2 = a2 + b2 arctan (y-component / x-component) : to find angle of resultant The Attempt at a Solution The...

Homework Statement Homework Equations Newton's 2nd Law The Attempt at a Solution I was wondering if anyone could verify that I have all the correct vectors or if I am missing any. I just wanted to check before I started trying to derive the equations. [/B]

What is the dimensionality, N, of the Hilbert space (i.e., how many basis vectors does it need)? To be honest I am entirely lost on this question. I've heard of Hilbert space being both finite and infinite so I'm not sure as to a solid answer for this question. Does the Hilbert space need 4...

You are given three vectors. A = 46.0 at θ1 = 56.6° above the +x axis B = 25.0 at θ2 = 34.4° above the −x axis C = 32.0 along the −y axis.Determine A - B + C (magnitude and angle from the positive x axis). Determine the angle relative to the positive x-axis, positive above and negative belowI...

Magnetic field lines around multipolar magnets get quite complex. There are local field vectors and field gradients in the x, y, & z plane. In the following diagrams I have tried to illustrate field lines around a centrally (half and half) charged disc magnet. The top diagram represents the...

Homework Statement A car is moving toward north with a speed of 35 km/h. A truck travels toward west with a speed of 42 km/h. Which is the speed of the caravan according to the car's driver? Homework EquationsThe Attempt at a Solution The solution given by the book is 15 m/s with direction...

What is the difference between scalars and one-dimensional vectors? I know that we represent the set of all two-dimensional vectors as ##\mathbb{R}^2##, so doesn't this mean that we would represent the set of all one-dimensional vectors as as just ##\mathbb{R}##? However, doesn't this also refer...

Homework Statement [/B] For the situation shown in the diagram, the block of mass m remains in place on the sloping front of the accelerating wedge, even though that sloping front is frictionless. Given these values, M = 20.0 kg, m = 4.00 kg, and theta= 34.0, calculate the net force acting on...

Homework Statement Find the magnitude and direction of the resultant of the following pair of forces: 60 N at 150 degrees to 20 N Answer: 43.8 N at 136.7 degrees to 20 N and 13.3 degrees to 60 N Homework Equations Cosine and sine rules: R2 = a2 + b2 - 2 * a * b * cos A a / sin A = b / sin b =...

Say I have an even-numbered set of vectors, X = \{x_1, x_2, ...x_{2n}\} where there exists some pairing of the vectors such that, x_iA = x'_i \quad \forall i=1..n However, I don't know what the pairing should be. Other than iterating over some norm and finding all pairs of i and j...

On a velocity-time graph, if an object is speeding up in the negative direction (let's say West), the acceleration that is calculated will be negative. To show the direction, would we put [West] or [East]? Also, if the object is slowing down in the negative direction (let's say West again)...

Homework Statement Show that if x^{\mu} is timelike and x^{\mu}y_{\mu}=0, y^{\mu}\neq 0, then y^\mu is spacelike. Homework Equations ds^2=\\>0\hspace{0.5cm}\text{timelike}\\<0\hspace{0.5cm}\text{spacelike}\\0\hspace{0.5cm}\text{lightlike} metric is diag (+---) The Attempt at a Solution Don't...

It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation. Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, ##|\psi_1,\psi_2>##. Each of these particles is moving in a...

Hi Guys, that's what i got <x,z>=<y,z> <x,z>-<y,z>=0 <x,z>+<-y,z>=0 <x-y,z>=0 x-y = [0,2,0] <2*[0,1,0],Z>=0 2<[0,1,0],z> = 0 <[0,1,0],z>=0 So 'im stuck at that. Any ideas?

Homework Statement Prove that a set of linearly independent vectors in Rn can have maximum n elements. So how would you prove that the maximum number of independent vectors in Rn is n?I can understand why in my head but not sure how to give a mathematical proof. I understand it in terms of the...

Hello! I am working on homework for my general relativity class, and I am very confused about how to tell the difference between spacelike, timelike, and null vectors, and the book is very unhelpful. Relevant equations Consider two four vectors a and b whose components are given by: a^α=(-2, 0...

I have two vectors: f1 = (x1,y1,z1) f2 = (x2,y2,z2) The origins are placed together and they are of the same coordinate system. They make a plane between the two vectors and the origin. How do you find the angle between the two vector on that plane?

Homework Statement The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...

For example if I have to find out work done.Force and displacement are given to be (2i^+3j^+4k^)and (-i^-2j^) respectively. till now i have been thinking that work done=Force multiplied by displacement cos theta but in my book in solution of the problem above work done is calculated by simply...

Homework Statement The Tensions in four cables are equal: |T1| = |T2| = |T3| = |T4| = T Determine the value of T so that the four cables exert a totl force of 12,500-lb magnitude on the support. (Inser a picture of 4 connected cables angled 9, 29, 40, 51 degrees respectively) My question...

Homework Statement A motorboat can move with a velocity of 10.0 m/s, with respect to the water in a river. The river is flowing at 4.00 m/s due east. (a) Calculate the direction (Give the angle with respect to one of the compass directions.) the motorboat must be pointed so that it moves due...

Homework Statement Three vectors A, B, C, each have a magnitude of 46 m and lie in an xy plane. Their directions relative to the positive direction of the x-axis are 28 ˚, 191 ˚, and 313 ˚. What are the magnitude and the angle of A-B+C with right-arrow in the range of (-180°, 180°)? Homework...

Homework Statement Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.7 cm . Two of the particles have a negative charge: q1 = -6.0 nC and q2 = -12.0 nC. The remaining particle has a positive charge, q3= 8.0 nC . What is the net...

Homework Statement [/B] Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units. a) find A dot B b) find A x B c)...

Homework Statement Vector P is a function of time t. In a specified coordinate system P is given by: P= (A+Bt)i + (A+Ct-Dt^2)j and P is in meters when t is seconds Given these values (shown without their units): A=15.0, B=7.00, C=20.0, D=4.00 (a) Calculate the time when P points in the...

Hello, PF! I had a quick question that I hoped maybe some of you could help me answer. The question is simple: Why is the cross product of two parallel vectors equal to the zero vector? I can see this easily mathematically through completing the cross product formula with two parallel...

Good afternoon, Question: Say I have an electromagnet at a 45 degree incline from an electron beam. This electromagnet is exerting 0.75 Tesla on the beam. How can I calculate the vector that the electromagnet will exert on a particle? Note, this is for my own curiosity, not for any homework...

MIT OCW 18.06 using Intro to Linear Algebra by Strang So I was working through some stuff about Cyclic Matrices, and the text was talking about how the column vectors that make up this cyclic matrix, shown here, are coplanar, and that is the reason that Ax = b will have either infinite...

1. Homework Statement Find forces P,F,and THomework Equations Fx = 0 Fy = 0 The Attempt at a Solution So far I only got force T from getting the moment from point b. Don't know how-to start getting force P and F since they're both at the same point. Any help will be much obliged thank you [/B]

Homework Statement The Vector a= -2i -3j and is orthogonal to vector b that has the same length as a. The third vector c has the dot products ca= 8m^2 and cb= 9m^2. What are the components of c? c = ______i + _____ j m Homework EquationsThe Attempt at a Solution I know that (a⃗ +b⃗ )⋅c⃗ =a⃗...

1. Homework Statement Given the two vectors in the diagram, calculate their magnitudes if A+B-225j=0 Homework Equations sum of x component= Acos(42)--Bcos(56) sum of y component= Asin(42)+Bsin(56)--225j The Attempt at a Solution Find A and B use substitution A= [Bcos(56)]/cos(42) from x...

Homework Statement Vector A has magnitude A = 4.0 units and is directed θA = 15◦ counterclockwise from the positive x-axis. Vector B has magnitude B = 4.0 units and is directed θB = 85◦ counterclockwise from the positive x-axis. Determine the following quantity: |A + B|^2 − |A − B|^2.Homework...

Homework Statement The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector. Homework Equations x = |R|cos(theta) The Attempt at a Solution I am confused about what degrees to input into the cosine function. I know that the vector is...

Homework Statement Suppose a linear transformation T: [P][/2]→[R][/3] is defined by T(1+x)= (1,3,1), T(1-x)= (-1,1,1) and T(1-[x][/2])=(-1,2,0) a) use the given values of T and linearity properties to find T(1), T(x) and T([x][/2]) b) Find the matrix representation of T (relative to standard...

Homework Statement Let B1={([u][/1]),([u][/2]),([u][/3])}={(1,1,1),(0,2,-1),(1,0,2)} and B2={([v][/1]),([v][/2]),([v][/3])}={(1,0,1),(1,-1,2),(0,2,1)} a) Show that B1 is a basis for [R][/3] b) Find the coordinates of w=(2,3,1) relative to B1 c)Given that B2 is a basis for [R[/3], find...

Use the component method to add the vectors A and B shown in the figure. Both vectors have magnitudes of 3.55 m and vector A makes an angle of $θ = 28.5°$ with the x axis. Express the resultant A + B in unit-vector notation. I don't understand how my answer is wrong. Isn't it $A + B =...

In Euclidean geometry, the Cauchy-Schwarz inequality is ##|e\cdot f| \le |e||f|##. In a Minkowskian signature, the inequality is reversed for timelike vectors. Apparently for spacelike vectors it depends on whether the two vectors span the light cone...

Somestimes, vectors (e.g <3,4>) are represented with a real and imaginary component (3 + 4i). When expressing wave phasors as vectors, this is usually the convention. Insofar as phasors and waves go, what rationale does the convention have? If I had to superimpose two waves together, and...

Homework Statement The figure depicts the sum of two velocities, vA and vB. The value of the sum is7 m/s and the angles shown in the image are θ1 = 29.8°, and θ2 = 18.3°. Homework EquationsThe Attempt at a Solution

Homework Statement The figure depicts the sum of two velocities, vA and vB. The value of the sum is7 m/s and the angles shown in the image are θ1 = 29.8°, and θ2 = 18.3°. Homework EquationsThe Attempt at a Solution I have no idea where to even begin on this

Homework Statement Let V be the set of all ordered pairs of real numbers. Suppose we define addition and scalar multiplication of elements of V in an unusual way so that when u=(x1, y1), v=(x2, y2) and k∈ℝ u+v= (x1⋅x2, y1+y2) and k⋅u=(x1/k, y1/k) Show detailed calculations of one case...

Homework Statement Force A has a magnitude of 200lb and points 35° N of W. Force B points 40° E of N. Force C points 30° W of S. The resultant of the three forces has a magnitude of 260lb and points 85° S of W. (a) What is the magnitude of Force B? (B) What is the magnitude of Force C...

The state, ##| S\rangle##, say, of a system is represented as a vector in a Hilbert space. ##\psi (x, t)## is the representation of the state vector in the position eigenbasis; ##\psi (p, t)## in the momentum eigenbasis et cetera. That is, ##\psi (x, t) = \langle x|S\rangle##; ##\psi (p, t) =...

The question is as follows: An object of mass m=1 follows the trajectory: r(t) = 4 ln(t) i + 6t1/2 j + 2t k Calculate the force acting on the object and hence find work done between t=1 and t=2. I know that Force = Mass * Acceleration Therefore, F(t) = 1 * a(t) I also know that a(t) =...

I have a question. Given a vector equation such as F = ma, how can we obtain a general expression for m, the mass? If the equation was scalar, this could easily be done by dividing F by a; however, we are dealing with vectors, and, to my knowledge, a vector divided by another vector is not...

Homework Statement To find the component of one vector A along another vector B. Homework Equations Components are A(cos theta) and A(sin theta) The Attempt at a Solution What I tried was to consider the vector B as a "pseudo x axis" and draw a subsequent "pseudo y axis". Then, using angle...

Homework Statement A car travels north with a velocity of 5.2-m/s for 92-seconds. It then turns east, and with the same speed travels for a further 22-seconds. Calculate the magnitude of the final displacement of the car. Now give the direction of the final displacement of the car. Give your...

Homework Statement Say you've been given vectors v1, v2 and v3. Homework EquationsThe Attempt at a Solution How do I construct a matrix out of these three vectors? Am I to use the given vectors as columns or rows in a matrix? When does this matter and when does it not? This may be a stupid...

Homework Statement Hi all, I have this quiz on MasteringPhysics, but I can't seem to get the right answer.[/B] Consider two positively charged particles, one of charge q0 (particle 0) fixed at the origin, and another of charge q1 (particle 1) fixed on the y-axis at (0,d1,0). What is the net...

I've been trying to figure out how to calculate if a satellite is in view of a ground station (and above a certain elevation) using just position vectors for both satellite and ground station. Does anyone know of an equation, algorithm, etc. that does this? Thanks