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Defines Length of a Vector in Rh, use your defination to give the formuls for the...
In Exercises 17-32, a vector u in R" and a subspace W of R" are given....
In Exercises 17-32, a vector u in R" and a subspace W of R" are given. (a) Find the orthogonal projection matrix Pw. (b) Use your result to obtain the unique vectors w in W and z in w such that u=w+z (c) Find the distance from u to W. 19. u = 2 and W is the solution set of the system of . equations X1 + X2 - X3 = 0 x1 - x2 + 3x3 = 0.
5. The electric field in a certain region of space is given by the vector field...
5. The electric field in a certain region of space is given by the vector field Vector E(Vector r)= Vector E(x,y,z)= (x-z)hatx+(z-y)haty V/m Find any two points P(x1,y1,z1) and Q(x2,y2,z2) such that the electric field at P is perpendicular to the electric field at Q. Evaluate the electric field at each of these two points. (Hint: Use the dot product.).
5. If ||2|| := VxTx is the usual (Euclidean) length of a vector x E R”,...
5. If ||2|| := VxTx is the usual (Euclidean) length of a vector x E R”, show that the vector Qx has the same length whenever Q is an orthogonal n xn matrix. If we define the angle between vectors x, y E R” as Z(x,y) := cos-1 -1 / xTy \ ||3||||y|| show that the angle between Qx and Qy is unchanged.
PROBLEM #2: Consider the metric: and vector: a) Compute the length-squared of the vector v. b)...
PROBLEM #2: Consider the metric: and vector: a) Compute the length-squared of the vector v. b) Using Mathematica, make a ContourPlot of the length of the vector in the x,y space. Comment about the result. Note, for this one, just focus on the first quadrant; I'll explain in class. c) Can you think of a physical example where this is the appropriate metric to use to measure distance??? There are more than one answer, but the more nat ural the...
I need help with this. Thank you for your time. 4.1 Consider the following two-dimensional vector...
I need help with this. Thank you for your time.
4.1 Consider the following two-dimensional vector fields: х F(x, y) = i + 1x² + y² х Ĝ(x,y) = i + (x2 + y2) Vx2 + y2 y 1x² + y² (x2 + y2 Sketch † (x, y) and Ĝ(x,y) on two separate graphs. Plot the field vectors at the following square grid of 25 points: The first upper row of points is (-2,2),(-1,2) (2,2) The last lower row of...
I just need help with part C. Mostly figuring out the sketch 2·[210 total points (practice with joint, marginal and con...
I just need help with part C. Mostly figuring out the
sketch
2·[210 total points (practice with joint, marginal and conditional densities) This is a toy problem designed to give you practice in working with a number of the concepts we've examined; in a course like this, every now and then you have to stop looking at real-world problems and just work on technique (it's similar to classical musicians needing to practice scales in addition to actual pieces of symphonic...
You are given a vector in the xy plane that has a magnitude of 81.0 units...
You are given a vector in the xy plane that has a magnitude of 81.0 units and a y component of -57.0 units. What are the two possibilities for its x component? Enter your answers using three significant figures separated by a comma. x1, x2 = 57.5,-57.5 units Assuming the x component is known to be positive, specify the magnitude of the vector which, if you add it to the original one, would give a resultant vector that is 80.0...
Find the magnitude and direction angle (to the nearest tenth) for the given vector. "Give the...
Find the magnitude and direction angle (to the nearest tenth) for the given vector. "Give the measure of the direction angle as an angle in 10, 360º). <-5, 12> magnitude (TIP: Remember magnitude is similar to length or distance.) direction angle • Use the form from class. If needed, round your answers to the tenths place.
Full working out and answers please. Exercises: A simple field which we often use is one...
Full working out and answers please.
Exercises: A simple field which we often use is one whose value at any point is just equal to the distance r of that point from the origin: T(x,y,z) = \x2 + y2 +:2 =r Sketch a contour map of this field on a plane through the origin. Calculate the gradient of this field and represent it as a vector quantity at a few points on your contour map
In Exercises 17-32, a vector u in R" and a subspace W of R" are given. (a) Find the orthogonal projection matrix Pw. (b) Use your result to obtain the unique vectors w in W and z in w such that u=w+z (c) Find the distance from u to W. 19. u = 2 and W is the solution set of the system of . equations X1 + X2 - X3 = 0 x1 - x2 + 3x3 = 0.
5. The electric field in a certain region of space is given by the vector field Vector E(Vector r)= Vector E(x,y,z)= (x-z)hatx+(z-y)haty V/m Find any two points P(x1,y1,z1) and Q(x2,y2,z2) such that the electric field at P is perpendicular to the electric field at Q. Evaluate the electric field at each of these two points. (Hint: Use the dot product.).
5. If ||2|| := VxTx is the usual (Euclidean) length of a vector x E R”, show that the vector Qx has the same length whenever Q is an orthogonal n xn matrix. If we define the angle between vectors x, y E R” as Z(x,y) := cos-1 -1 / xTy \ ||3||||y|| show that the angle between Qx and Qy is unchanged.
PROBLEM #2: Consider the metric: and vector: a) Compute the length-squared of the vector v. b) Using Mathematica, make a ContourPlot of the length of the vector in the x,y space. Comment about the result. Note, for this one, just focus on the first quadrant; I'll explain in class. c) Can you think of a physical example where this is the appropriate metric to use to measure distance??? There are more than one answer, but the more nat ural the...
I need help with this. Thank you for your time.
4.1 Consider the following two-dimensional vector fields: х F(x, y) = i + 1x² + y² х Ĝ(x,y) = i + (x2 + y2) Vx2 + y2 y 1x² + y² (x2 + y2 Sketch † (x, y) and Ĝ(x,y) on two separate graphs. Plot the field vectors at the following square grid of 25 points: The first upper row of points is (-2,2),(-1,2) (2,2) The last lower row of...
I just need help with part C. Mostly figuring out the
sketch
2·[210 total points (practice with joint, marginal and conditional densities) This is a toy problem designed to give you practice in working with a number of the concepts we've examined; in a course like this, every now and then you have to stop looking at real-world problems and just work on technique (it's similar to classical musicians needing to practice scales in addition to actual pieces of symphonic...
Find the magnitude and direction angle (to the nearest tenth) for the given vector. "Give the measure of the direction angle as an angle in 10, 360º). <-5, 12> magnitude (TIP: Remember magnitude is similar to length or distance.) direction angle • Use the form from class. If needed, round your answers to the tenths place.
Full working out and answers please.
Exercises: A simple field which we often use is one whose value at any point is just equal to the distance r of that point from the origin: T(x,y,z) = \x2 + y2 +:2 =r Sketch a contour map of this field on a plane through the origin. Calculate the gradient of this field and represent it as a vector quantity at a few points on your contour map
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