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Scalar and Vector Operations

In physics problems, it is important to recognize when working with scalar or vector operations, as this can dramatically change the results. Scalar quantities are given by a data point, such as temperature, whereas vector quantities are given in a three-dimensional space, such as velocity. Preforming mathematical operations to a scalar quantity is simple. Just carry out the operation as normal and carry and convert the units. A vector quantity requires the direction of the vector to be taken into consideration.

Scalar quantities only deal with the magnitude of the medium. Scalar quantities is generally what is used. Time, volume, speed and temperature are common scalar quantities. They are just a data point with no respect to any direction. Vector quantities are what indicate direction and can become more complex in the mathematical computation. Increase/Decrease in temperature and velocity are common examples of vector quantities. It is possible to multiply a scalar and vector quantity together. The resulting quantity will be a vector.

Vector addition: Hiker's displacement

Path A is 9.0 km long heading 60.0° north of east. Path B is 6.0 km long in a direction due east. Path C is 3.0 km long heading 315° counterclockwise from east. (a) Graphically add the hiker's displacements in the order A, B, C. What is the magnitude of displacement in km? Direction of displacement? (b) Graphically add t

Vector Common Point Angles

When two vectors A and B are drawn from a common point, the angle between them is (phi) . If A and B have the same magnitude, for which value of (phi) will their vector sum have the same magnitude as A or B? --------------------------------------------------------------------------------------------------- Three hori

Mass in metric, mass vs weight, law of motion, net force, vector

1. Answer the following: a. What are the units of mass and the units of weight for the metric system? b. What are the units of mass and the units of weight for the English system? 2. Explain the relationship between the mass and the weight of an object. Is the mass of an object the same on earth and the moon? Are the wei

Vector A and B problems

1. Vector A = 119 grams @ 164°. What is Ax ? 2. Vector A = 119 grams @ 164°.What is Ay ? 3. Vector B = (114) xunit vector + (-32.8) yunit vector. Assume [grams] as the unit. What is the magnitude of B? 4. Vector B = (114) xunit vector + (-32.8) yunit vector. Assume [grams] as the unit. What is the direction of B in ra

Cubic and Orthorhombic Crystals

Show that the general direction [ hkl ] in a cubic crystal is normal to the planes with Miller indices (hkl). Is the same true in general for an orthorhombic crystal? Show that the spacing d of the (hkl) set of planes in a cubic crystal with lattice parameter a is: d = (a)/(h^2 + k^2 +l^2)^(1/2) What is the generaliza

Eigenvalues and Eigenvectors of a Hermitian Matrix

Please see the attached file for the full problem statement, and please show all steps in your solution. Consider the Hermitian matrix omega = 1/2 [2 0 0 0 3 -1 0 -1 3] (1) Show that omega1 = omega2 = 1; omega3 = 2. (2) Show that |omega = 2> is any vector of the form 1/((2a^2)^(1/2)) [0 a -a] (3) Show that t

Vector space: null vector and inverse of a vector

Consider the set of all entries (a,b,c) where the entries are real numbers. Addition is defined as: (a,b,c)+(d,e,f) = (a+d,b+e, c+f) Scalar multiplication is defined as: x(a,b,c) = (xa,xb,xc) Write down the null vector and inverse of (a,b,c). show that the vectors (a,b,c) do not form a vector space.

The magnitude of a vector can in general be define as A = (A.A)^1/2.

A) The magnitude of a vector can in general be define as A = (A.A)^1/2. Write a function which finds the magnitude of a general vector using Mathematica. b) Using the definition of the dot product A·B = A B cos(θ), and your function in part a), write a function to find the angle in degrees be

Vectors

let vector a=15i -40j and vector b=31i +18k. find vector c such that vectors a+b+c=0

Physics

Hello I need help answering these problems. Peter noticed a bug crawling along a meter stick and decided to record the bug's position in five-second intervals. After the bug crawled off the meter stick, peter created the table shown. 1. What is the displacement of the bug between t = 0.00 s and t = 20.0 s? 2. what is the to

Divergence theorem for a function

1. Check the divergence theorem for the function: V(vector)= r^2*cos(theta)(r(hat))+r^2*cos(phi(Theta(hat)) -r^2*cos(theta)*sin (phi)(phi(hat)) Use as the volume one octant of the sphere of radius R

Divergence and Curl of a Vector Function

Given the vector function V = {-y/[(x-4)^2+y^2)]^3/2 + (x+4)/[(x+4)^2+y^2)]^3/2}*xhat +{(x-4)/[(x-4)^2+y^2)]^3/2 + y/[(x+4)^2+y^2)]^3/2}*yhat a) What is the divergence at (-4,0) b) What is the curl at (4,0)

divergence of a vector function

Given vector function V = xyi +2yzj+3zxk, what is the divergence of this function? is the magnitude of the divergence greater at the origin or at (1,1,1)

Gradient Determination of Functions

Calculate the gradient Vf of the following functions, f(x,y,z) a. f = x^2 + z^3 b. f = ky where k is a constant c. f = r = (x^2 + y^2 + z^2)^1/2 Hint use the chain rule d. f = 1/r See attachment for better symbol representation

Plane Wave Propagation

Please see the attached file for a full description of the problem. Consider a unit vector s = , and a plane perpendicular to s at a distance d from the origin. a. For all points r within this plane, show that r.s = x sz + y sy + z sz = d. b. Show that the scalar function f (x, y, z, t) = exp(i 2 pi (xsx + ysy + z sz)/L -

Addition of spin angular momenta

Addition of spin angular momenta Consider the addition of two spin -1/2 angular momenta, S(1) and S(2) 1. How many states are there in the product basis? 2. If J = S(1) + S(2), what are the possible eigenvalues of the dot product of J and J? 3. By using the recursive algorithm construct all the Clebsch-Gordan coefficient

Eigenvalues, eigenvectors, and time evolution.

Dear Mitra, I in fact wrote the wrong matrix but I am still confused after PART A. (PART A) The actual matrix is: H = 1 2 0 2 0 2 0 2 -1 Where the eigenvalues are E1 =0, E2=3hw, E3=-3hw and as you said the trace(H) =0 = sum of eigenvalues. I also found the eigenvectors using Hx = Ex and they w

Westward component

A soccer player carries the ball for a distance of 40.0 m in the direction 42.0 west of south. Find the westward component of the ball's displacement. 26.8 m 29.7 m 36.0 m None of the other choices is correct.

The answer to Resultant Force

Three forces are acting on the origin. F1 has a magnitude of 70 N and is 30 degrees north of east. F2 has a magnitude of 70 N and is 30 degrees north of west. F3 has a magnitude of 70 N and is along the south direction. Find the resultant force acting on the origin.

Vector transformation

Consider a two-dimensional spatial coordinate system S' whose coordinates (u,v) are defined by x = u + v y = u - v in terms of the coordinates of a Cartesian coordinate system S. Suppose you are given a vector in S whose contravariant components are Am = (2,8). Determine the contravariant components of this ve