Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if...
Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if you are in a room with walls, ceiling and floor. The edges are x, y and z with z up toward the ceiling, the flat plane floor is x-y.
Starting at the origin, go along "x" 2 meters. Then go parallel to "y" 3 meters. Then go up parallel to "z" 2 meters. This point is somewhere in the room above the floo
- What is the vector from the origin to the point?
- What is the magnitude of that vector? That is, what is its length?
- What angle does it make to the floor? This would be 90°-θ where θ is the angle down from the z azis. (Hint: Use the arctangent knowing z and the length of the vector.)
- If you dropped from that point directly down to the floor, how far would you fall?
- How long would it take, given that falling objects accelerate at 10 m/s every second (10 m/s2)?
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Imagine a 3-dimensional world with coordinates that are labeled with x, y, and z, as if...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z)...
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addi...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
+z X ya +y +x -Z Consider the three-dimensional coordinate system where x goes toward you...
+z X ya +y +x -Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and a goes up and down with and directions as shown. At one point in time an electromagnetic wave is moving in the direction and has its E- field in the -z direction. In which direction is B-field at the same point in time? y direction +y direction +x direction - direction O +z direction
Ah arbnrary number nents, and all 2-companents separately to f of vector ately to find x-, y"r z-...
how do you do 7 and 8 ?
ah arbnrary number nents, and all 2-companents separately to f of vector ately to find x-, y"r z-components of the resultant vector. B) Break the (given) vectors down into their x-, y, and 2-componerto c) Combine total x, y-, and z-components using Pythagorean Thetee sine the resultant vector and use tangent to determine its angle. and cosines nd the magnitude of Graphical Representation of Vectors You will need o ruler, graph poper,...
help please. +z -X +y +x Z Consider the three-dimensional coordinate system where x goes toward...
help please.
+z -X +y +x Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and z goes up and down with + and directions as shown. At one point in time an electromagnetic wave is moving in the - direction and has its E-field in the -z direction. In which direction is B-field at the same point in time? +2 direction -y direction -z direction
+z -ya- +y +x V -Z Consider the three-dimensional coordinate system where x goes toward you...
+z -ya- +y +x V -Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and z goes up and down with + and directions as shown. At one point in time an electromagnetic wave is moving in the - direction and has its E-field in the - direction. In which direction is B-field at the same point in time? O +z direction +y direction -y direction O - direction...
how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin
how do you find the coordinates of the point (x, y, z) on the plane z = 1 x + 1 y + 2 which is closest to the origin
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- ...
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- termine the velocity vector v(t) in terms of φ and θ if it is constantly moving at the speed 5m/s, along the direction (φ,0). Here, φ denotes the angle between the z-axis and the projection of the position vector r(t) on the xy-plane; meanwhile θ denotes the angle between the z-axis and r(t). You may assume that (φ, θ) are fixed over time at...
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are...
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are given in the figure. Each vector field has zero z-component (i.e., all of its vectors are horizontal) and is independent of 2 (i.e., is the same in every horizontal plane). You may assume that the graphs of these vector fields use the same scale. (a) Are div(F) and div(G) positive, negative, or zero at the origin? Be sure you can explain your answer. At...
Two charges are placed on the y axis. One charge is -1.04E-9 coulombs at (x,y)=(0,+3) cm...
Two charges are placed on the y axis. One charge is -1.04E-9 coulombs at (x,y)=(0,+3) cm and the other +1.04E-9 Coulombs at (x,y)=(0,-3)cm. What is the direction of the net electric field at the point (x,y)=(4,0)cm? A, straight up, parallel to the positive y axis B. straight down, parallel to negative y axis c. along the x direction d. along the negative x direction What are the distances of the charges form the point (4,0) cm in meters?
Problem 3. (1 point) The temperature at a point (X,Y,Z) is given by T(x, y, z) = 200e-x=y+14–2–19, where T is measured in degrees Celsius and x,y, and z in meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector. Find the rate of change of the temperature at the point (-1, 1,-1) in the direction toward the point (-4,-5, -5). In which direction...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
+z X ya +y +x -Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and a goes up and down with and directions as shown. At one point in time an electromagnetic wave is moving in the direction and has its E- field in the -z direction. In which direction is B-field at the same point in time? y direction +y direction +x direction - direction O +z direction
how do you do 7 and 8 ?
ah arbnrary number nents, and all 2-companents separately to f of vector ately to find x-, y"r z-components of the resultant vector. B) Break the (given) vectors down into their x-, y, and 2-componerto c) Combine total x, y-, and z-components using Pythagorean Thetee sine the resultant vector and use tangent to determine its angle. and cosines nd the magnitude of Graphical Representation of Vectors You will need o ruler, graph poper,...
help please.
+z -X +y +x Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and z goes up and down with + and directions as shown. At one point in time an electromagnetic wave is moving in the - direction and has its E-field in the -z direction. In which direction is B-field at the same point in time? +2 direction -y direction -z direction
+z -ya- +y +x V -Z Consider the three-dimensional coordinate system where x goes toward you and away from you, y goes right and left, and z goes up and down with + and directions as shown. At one point in time an electromagnetic wave is moving in the - direction and has its E-field in the - direction. In which direction is B-field at the same point in time? O +z direction +y direction -y direction O - direction...
(a) Consider a particle which starts moving around from the origin in a 3-dimensional space. De- termine the velocity vector v(t) in terms of φ and θ if it is constantly moving at the speed 5m/s, along the direction (φ,0). Here, φ denotes the angle between the z-axis and the projection of the position vector r(t) on the xy-plane; meanwhile θ denotes the angle between the z-axis and r(t). You may assume that (φ, θ) are fixed over time at...
(1 point) Horizontal cross-sections of the vector fields F(x, y, z) and G(x, y, z) are given in the figure. Each vector field has zero z-component (i.e., all of its vectors are horizontal) and is independent of 2 (i.e., is the same in every horizontal plane). You may assume that the graphs of these vector fields use the same scale. (a) Are div(F) and div(G) positive, negative, or zero at the origin? Be sure you can explain your answer. At...
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