Calculate the divergences of cach of the following vectors:(a) v = 3k(b) v = r(c) = (4xz + y?) î + (12a² – 2²) ĵ + (xy – yz) k(d) ở = -yî+ x}(c) v = .-

Since you have posted multiple questions, according to company policy we will answer only the 1st…

Answered: Calculate the divergences of cach of…

Calculate the divergences of cach of the following vectors: (a) v = 3k (b) ở = r (c) v = (4xz + y²) î + (12.a² – 2²) ĵ + (xy – yz) k %3D %3D -

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.35P

See similar textbooks

Related questions

Q: etermine the mechanical energy, kinetic energy, a

A: We know that the mechanical energy of a system is generally in terms of potential energy and kineti...

Q: Four particles enter a region of uniform magnetic field with velocities perpendicular to magnetic fi...

Q: A 3.65x10-12 C is placed inside a cube what is the amount of electric flux passing through each side

Q: The elasticity of a good is E=0.2. by (a) A 3% price increase will cause the demand to -Select--- %....

Q: A train is 350 meters long goes through a tunnel that is 2.52 kilometers long how long does the trai...

A: Given in question: Length of tunnel(L) = 2.52 Km = 2520 m Length of ...

Q: What is the magnitude of electric force exerted on a proton 5 x 10-8 m away from the electron? Base...

A: Given information: The distance between proton and the electron (r) = 5 x 10-8 m General information...

Q: Q3) a) The critical angle for total internal reflection at a liquid-air interface is 42.5°. (i) If a...

A: Note : we can answer only 1 question and it's related sub-parts. Please, post other question in next...

Q: 11. Find e (in degrees). (0.35m, 0.49m) Knee Ankle (0.1m, 0.15m)

A: GivenCoordinates of Ankle (x1,y1) = (0.1 m, 0.15 m)Coordinates of Knee (x2,y2) = (0.35 m, 0.49 m)

Q: Aparticle with a mass of 1,81 g and a charge of -2,50 nC. The particle moves with a velocity of 4,00...

A: Determine the force on the particle.

Q: 11. An electric field of 600V/m is desired between two parallel plates 137.0mm apart. What voltage s...

Q: Two converging lenses, each of focal length 14.9 cm, are placed 39.6 cm apart, and an object is plac...

Q: A 70- kg man can store about 120000 kcal of energy as fat. How far could such a man run on this sto...

Q: An object 1.1 cm high is viewed under a magnifier of focal length 14 cm by a person with a near poin...

Q: A total charge of 300 nanocoulombs is distributed evenly throughout the area of a disk with radius 1...

Q: If a radioactive isotope of thorium (atomic number 90, mass number 232) emits 4 alpha particles and ...

A: When any radioactive elements emit alpha particle, it's atomic number reduces by 2 and mass number r...

Q: In the figure, a 2.8 g ice flake is released from the edge of a hemispherical bowl whose radius r is...

Q: Part 2 Voltage, V Plate Area, A 1.5V 200mm^2 %3D Table B Plate Separation, d [millimeter, mm] Capaci...

A: You asked to plot 'Q' vs 'd' hence we will take 'Q' on x-axis and 'd' on y-axis.

Q: ay to increase the magnitude of electric force? Group of answer choices increase the distance betwee...

A: We know that the formula of the electric force is given as F = kq1q2r2 here q1 q2 is the charge r ...

Q: How much work is required to stretch a spring from x-4.5 cm to x=8.2 cm given a spring constant of 1...

A: GivenSpring constant (K) = 150 N/mX1 = 4.5 cm = 4.5 ×10-2 mX2 = 8.2 cm = 8.2 × 10-2 m

Q: Three point charges of 1 C, 2°C and 3 C are placed at the corners of an equilateral triangle of side...

Q: Determine the electric potential difference between (−5,0,1) and N( 2, −2, −2) given two point charg...

Q: Two positive charges q1 and q1 are separated by a distance r. The charges repel each other with a fo...

A: Initial force, F = kq1q2/r2 Now r' = r/4 => F' = kq1q2/r'2 = kq1q2/(r/4)2 = 16 kq1q2/r2 => F' ...

Q: An electron, initially at rest is placed in an electric held of 5x10 N/C directed west. What is the ...

A: Given in question: Electric field(E) = 5x10 N/C = 50 N/C To find: What is the acceleration of the el...

Q: Match each force diagram in group I from diagram with a 2 that shaws graup the same net force

A: To solve for the net force, we resolve all the forces that are acting into components in the X and Y...

Q: Problem 7: A power line carries a DC current of I = 25 A in a direction ø = 27° east of magnetic nor...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and ...

Q: A. from paper to glass B. from rubber to silk C. from silicon to copper D. from nylon to steel

A: Given : Tend to lose electrons of a body is large means it can easily give electrons to other body ....

Q: 7. An electric flux of 8.99x10-12 Nm2/C is passing through a sphere created by 1.25x10-3 N/C electri...

A: Write the expression for the electric flux. Here, E is the electric field, A is the area of the sph...

Q: A flat sheet of paper with dimensions 50 m x 60 m is oriented so that the normal to the sheet is at ...

A: If the area of the sheet of paper is A and electric field of magnitude E applied at an angle of "the...

Q: View Policies Current Attempt in Progress Find the magnitude of the current in the 2.0-Q resistor in...

Q: Let's use a simple example. Say a steel ball with a mass of 0.580 kg is initially at rest. It is the...

A: Provided that Mass of ball(m) =0.580kg Initial velocity(v)=0m/s Height (h)=1.50m 1) Applyin...

Q: Calculate the work for the expansion of 3 moles of B,H; at 40°C from 2.74 L to 3.89 L using van der ...

A: We know that We have given a general equation of the van der Waals is given as P+anv2vn-b= RT We ...

Q: What is the x-component of a vector with a magnitude of 73 cm, 41° South of eas

A: Given: The magnitude of the vector is 73 cm. The direction of the vector is 41o South of East. The d...

Q: 41. Velocity at the Equator The earth rotates through one complete revolution every 24 hours. Since ...

Q: An electric flux of 8.99x102 Nm²/C is passing through a sphere created by 1,25x10 N/C electric held....

Q: An open pipe has a piston inserted into one of its ends. A tuning fork with the frequency of 342 Hz ...

Q: If a test charge of 12 µC is in a electric field that produces 8 uN, and the distance 2.3 mm from an...

A: Given: q=12μC=12*10-6 CF=8μN=8*10-6 Nd=2.3 mm=2.3*10-3 m

Q: マ-vs thin cylinder towards of mass M and Radins R which is mounded on fixed vertical axis d <R. M is...

Q: A satellite is in a circular orbit around the Earth at an altitude of 4.00 x 106 m. (a) Find the pe...

A: Given, A satellite is in a circular orbit around the Earth at an altitude of, h = 4.00×106 m radius ...

Q: a) Find the far point of an eye for which a prescribed lens has an optical power of -0.56 d. (b) F...

A: The power of the lens is defined as the ability of a lens to bend the light rays at a particular poi...

Q: The range of the ball is always measured starting from the edge of the table up to the position wher...

A: The range of the ball is always measured starting from the edge of the table up to the position wher...

Q: Does the magnetic field increase or decrease when you get close to the magnet?

A: Magnetic field is inversely proportional to distance from magnet. As we are getting closer, distance...

Q: 12. Three identical wires carry equal current of 4.0 A that is coming out of the plane of the page. ...

Q: 2. A soccer ball is kicked into the air so that the path of its flight can be modeled by the functio...

Q: What is the plate area if both of the plates are separated by a distance of 3.4nm and the capacitanc...

Q: Since the initial potential energy and final kinetic energy are zero, our equation now becomes EP,f ...

Q: One hazard of space travel is debris left by previous missions. There are several thousand objects o...

Q: An automobile starts from rest and reaches a sp of 42 m/s in 15 seconds. The acceleration increases ...

A: We know that the first equation of motion is given as v = u+at here u is the initial velocity v i...

Q: An electron, initially at rest is placed in an electric field of 5 ×105 N/C directed to the west. W...

A: The force on the charge particle is F = qE Where q is the charge on electron its v...

Q: 24. What happens to the electric force between two charged objects if the distance between them is r...

Q: Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wa...

A: Force ( F1 ) = 75 N Force ( F2 ) = 93 N Friction force = 12 N Mass of third child and wagon = 27 ...

Concept explainers

Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

Calculate the divergences of cach of the following vectors:
(a) v = 3k
(b) v = r
(c) = (4xz + y?) î + (12a² – 2²) ĵ + (xy – yz) k
(d) ở = -yî+ x}
(c) v = .
-

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6) . Find y y and r .
Is it possible for to be smaller than unity? `
What surface is represented by r a = const, that is described if a is a vector of constant magnitude and direction from the origin and r is the position vector to the point P(x1, x2, x3) on the surface?
The functions ¢1(x) and ø2(x) are normalized: d φ( (α) φι(α) dx 0(x) 62(x) = 1 = 1 -00 -00 and are mutually orthogonal dx oi(x) $2(x) dx 4i(x) $1(x) = 0 . Is the function b_(x) = ¢1(x) – $2(x) normalized? If not, determine its normalization constant and write the formula for the normalized y_ (x). Is the function +(x) = ¢1(x) + ¢2(x) %3D orthogonal to _(x)?
Problem 7: Two vectors in Cartesian coordinates have components A = (3, 2, 3) and B = (4, -1,7). What is the dot product of vector A with vector B? A B = | sin() cotan() atan() cosh() cos() asin() acotan() tanh() O Degrees tan() acos() sinh() cotanh() Radians П () 7 8 E ^^ 4 / 1 + * 5 2 0 BACKSPACE 963 HOME END DEL CLEAR
Problem 8: Two vectors in Cartesian coordinates have components A = (1, 3, 2) and B = (4, 2, 5). IAI = Part (a) What is the length of the vector A? sin() cotan() atan() acotan() tanh() cosh() O Degrees Hints: 0% deduction per hint. Hints remaining: 1 cos() asin() Submit ♫ tan() acos() E sinh() cotanh() Radians Hint Part (b) What is the length of the vector B? Part (c) What is the angle, in degrees, between A and B? ^^^ 1 + * 7 4 1 Feedback 0 8 5 2 VBACKSPACE 9 63 های HOME END DEL CLEAR I give up! Feedback: 0% deduction per feedback.
(b) Sphericals x=r sine coso y=r sine sino z=r cose Consider spherical coordinates as defined by their relationships to the Cartesian coordinates: x =r sin 8 cos p X2 =r sin 0 cos X3 =r cos 0 r2 = [xỉ + x3 + x e = tan-(x? + x3)x3 $ = tan-(x2/x1) or
(6%) Problem 5: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k В = -6. 5i + 7.1j + 10.2k 25% Part (a) What is the x-component of the vector V = 3(A × 2B)? Vx= sin() cos() tan() 7 8 9 НOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 cosh() tanh() cotanh() + END Degrees Radians Vd BACKSPACE DEL CLEAR Feedback Submit Hint I I give up! Hints: 2 for a 0% deduction. Hints remaining: 0 Feedback: 3% deduction per feedback. -This is a cross-product, so the answer will be a vector. In this part, we just want the x-component of the vector. Keep in mind that scalars like "2" and "3" distribute 3.
Vector A has magnitude 5.00 m and lies in the xy-plane in adirection 53.0o from the +x-axis axis measured toward the +y-axis.Vector b has magnitude 8.00 m and a direction you can adjust. (a) Youwant the vector product A : B to have a positive z-component of thelargest possible magnitude. What direction should you select for vectorB S? (b) What is the direction of B for which A : B has the mostnegative z-component? (c) What are the two directions of B S for whichA : B is zero?
Let a = (a)a + b and a-b b (b)-2ā + (c) The magnitude of a and b (d)a × b (e) Show that a. (axb) = 0 and b. (axb) = i-2j-2k and b= 61+31 + 2k; Find?
For the two vectors: (vectors)G= 2ˆi-3ˆj+1ˆk and (vector)H= 2ˆi+1ˆj-1ˆk what is (vector)G· (vector)H? Whatis the angle between (vector)Gand (vector)H?
518۹ من ٥۱۹۰ Example 2; find O between A¯and B? A*=2î +3ƒ +k , B =3î -2j +k Example 3; if 0=30o between A¯and B'find q value? A¯=2î +2j +4k , B'=qî +j -2k Example 4; Find the angle between the vectors A¯=2î +3ƒ +1k , B` =-4î +2ƒ -1k منو يعرف يحل ذني الاسئله مالت الفيزياء de between4md 8 agnitude 2 and vect he angle a between 90, or 180. following situations must be. On each sit an one correct answ C , (c) A 8-6 B=30 betweenA"an d the angle between t N--4i +2 -1 دعاء صاحب حسین 4:19p äclul 21.02.04 II