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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

Work, vectors, and kinetic energy

4. A 1.5 kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0m? 5. If the vectors A and B have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is -100, what

displacement vector and distance

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

Curves in euclidean 3-space

In Euclidean three-space, let p be the point with coordinates (x,y,z) = (1,0,-1). Consider the following curves that pass through p: Curve 1: xi (λ) = (λ, (λ-1)2, - λ) Curve 2: xi (μ) = (cos μ , sin μ, μ-1) Curve 3: xi (σ) = (σ2, σ3 + σ2, σ) The curves are parametrized by the parameters that v

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

Velocity of a charge moving in a magnetic field

The problem states: A particle with a charge of -5.90 * 10^-9 C is moving in a uniform magnetic field B(vector) = -(1.25 T) k (hat). The magnetic force on the particle is measured to be F(vector) = -(4.00 * 10^-7 N) i(hat) + (7.60 * 10^-7 N) j(hat). 1. Are there components of the velocity that are not determined by the

Vectors and Unit Vector

The vector A has a magnitude of 3.00 meters. It makes an angle of 30° with respect to the positive x-axis. The vector B has a magnitude of 3.00 meters, but points along the y-axis. What are the horizontal and vertical components of ? a) Ax = 2.60, Ay = 1.50 b) Ax = 1.50, Ay = 2.60 c) Ax = 3.00, Ay = 3.00 d) Ax = -2.

Resultant Vectors of 3 Displacement Vectors

How do I find the resultant of the three displacement vectors in the drawing by means of the component method? If the magnitudes of the vectors are A= 5 m B=5 m and C= 4 m?

Magnitude of Displacement Vector

An ocean liner leaves New York and travels 18.0 degrees north of east for 155 km. How far east and how far north has it gone? How do I figure out the magnitudes of the ships displacement vector in the directions due east and due north?

Magnitude and Direction of a Resultant Vector

If Displacement vector A points due east and has a magnitude of 2.00 km. Displacement vector B points due north and has a magnitude of 3.75 km. Displacement vector C points due west and has a magnitude of 2.50 km. Displacement vector D points due south and has a magnitude of 3.00 km. How can I find the magnitude and direction (

Pair of forces

Consider a pair of forces, one having a magnitude of 20 N, and the other having a magnitude of 12 N. What maximum net force is possible for these two forces? What is the minimum net force possible?

electric field and potential of point like charges.

(See attached file for full problem description) --- Two equal, positive charges, q = 2.0 micro Coulomb ; are located on the x-axis- one at +0.3m and the other at -0.3m. A third charge Q = +4.0 micro Coulomb is located on the y-axis at +0.4m 1) Find the magnitude & direction of the resultant (net) force on Q. 2) Find

Stokes and Gauss' Theorem

1. A vector field v(x, y, z) is given by the formula v(x, y, z) = xyˆx − yˆ2y. Consider a square path in the xy plane which starts at (0,0,0) and moves along the corners (1,0,0), (1,1,0) and (0,1,0). Calculate the path integral of v, i.e. v · dr, and calculate the area integral of the divergence, R ∇ × v · da, an

Center of Mass of Particles

A) Find the xcm coordinate of the center of mass of the system of particles shown in the figure. (See attached file for full problem description with diagram and values) Express your answer in meters to two significant figures. xcm = B) A straight rod has one end at the origin and the other end at the point (L,0) and

Center of Mass and Coordinate System

A system of four buckets forms a square as shown in the figure. Initially, the buckets have different masses (it is not known how these masses are related). A student begins to add water gradually to the bucket located at the origin. As a result, what happens to the coordinates of the center of mass of the system of buckets? (Se

Force; Calculating X and Y Components of a Quadrant

Could you show me how to perform the calculation asked for? It is part B. Calculate the theoretical x and y components of the first quadrant force vector using the cosine and sine of the measured angle and the measured first quadrant force. Then compare these values to the experimental scale readings along the x and y directi

Scalar and vector operations

(See attached file for full problem description with proper symbols) 1. Write each vector in terms of the unit vectors ^i and ^j. 2. Use unit vectors to express the vector C, where C = 3.00A - 4.00B. 3. Find the magnitude and direction of C.

Three problems on electrostatics

(See attached file for full problem description) --- 4 a) Sketch arrows on the diagram (see attachment) to indicate the direction of the electric field, if any, at each of the points A, B, C, and D. A positively charged test particle is observed to move as described below. For each motion, tell whether the work done by