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Question 2: Consider the points located at A(1,1,1), B(2,2,3) and C(6,1,10). a) Find the true angle...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C"...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
7. (10 points) Consider the cube with the eight vertices (+1, +1, +1). Let A, B,...
7. (10 points) Consider the cube with the eight vertices (+1, +1, +1). Let A, B, and C be the midpoints of the three edges that join with the vertex (1,1,1). (a) What are the coordinates of A, B, and C? (b) What is the equation of the plane through A, B, and C? (c) What is the angle between the plane in (b) and the face x=1 of the cube?
a，b and c，completed processes 134. Idempotent Transformations. Find the matrices of the transformations T which or...
a，b and c，completed processes
134. Idempotent Transformations. Find the matrices of the transformations T which orthogonally project a point (r,y, z) onto the following subspaces of R3. Show by two methods that each transformation is idempotent (i.e., T o T = T). (a) The z-axis. (b) The straight line r-y-2z. (c) The plane 0. + y + z
134. Idempotent Transformations. Find the matrices of the transformations T which orthogonally project a point (r,y, z) onto the following subspaces of...
I have attached the questions and the final solutions. Please do all of questions 7 and 8 7. Given the line L:x,y,z-2,2,3+1,-1,-3, the plane S 3x-2y+2z-7 and the point A 1,1,1 a) Find parametric equ...
I have attached the questions and the final solutions. Please do
all of questions 7 and 8
7. Given the line L:x,y,z-2,2,3+1,-1,-3, the plane S 3x-2y+2z-7 and the point A 1,1,1 a) Find parametric equations of the line which contains the point A, intersects the line and which is parallel to the plane b) Find parametric equations of the lne which contains the point A and which intersects the line Lat the&angle a) Show that V" is a subspace of...
Consider the angle shown below with its vertex located at -2,-2). The circle centered at the...
Consider the angle shown below with its vertex located at -2,-2). The circle centered at the angle's vertex has a radius 3 units long, and the terminal point is at (0.13, – 4.12). -6 -5 -4 -3 -2 -1 1 2 - 0.13, -4.12) What is the angle's radian measure (assuming that 0 < < 2)? o= Preview Submit License Question 13. Points possible: 1 Unlimited attempts. Message instructor about this question
Question 1 (2+2+5 marks] (a) Find the angle between the vectors y =(4,0,3), v = (0,2,0)....
Question 1 (2+2+5 marks] (a) Find the angle between the vectors y =(4,0,3), v = (0,2,0). (b) Consider the subspace V (a plane) spanned by the vectors y, V. Find an orthonormal basis for the plane. (Hint: you may not need to use the full Gram-Schmidt process.) (c) Find the projection of the vector w=(1,2,3) onto the subspace Vin (b). Hence find w as a sum of two vectors wi+w, where w, is in V and w, is perpendicular to...
Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a)...
Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a) [4pt] Determine vanishing point of the line when centrally projected onto the plane z = 2: Vanishing point: 10)a)ii) (4pt] Graph the central projection of the line onto the plane z = 2. y 6 2 2 8 -6 -4 -2 0 2 8 -2 61
PROBLEM 2 (15 points) (A) Consider the configuration displayed in Fig. la. Two charges of value...
PROBLEM 2 (15 points) (A) Consider the configuration displayed in Fig. la. Two charges of value q are placed at the vertices A and B of an equilateral triangle. Vertex C is at the origin of the coordinate system (0,0,0). Edge AB is in the ry plane and perpendicular to the a axis. Calculate the electric field at vertex C (B) Consider that the triangle is rotated by an angle ф around the z axis, as shown in FigFig. 1b,...
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the...
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the vertices of a rectangle in 3D space. Q7)a) [12pt] Complete the below table by calculate the central and parallel projections of these points onto the plane z = 1. Point Central projection onto z=1 Parallel projection onto z (-4,4,2) (4,4,2) (4, -4,4) (-4,-4,4) Q7)b) (8pt] Sketch both the centrally projected rectangle and the parallel projected rectangle on the coordinate planes below (be sure to...
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z = 3. (a) Find its moment...
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z = 3. (a) Find its moments and products of inertia relative to the origin. (b) The particle undergoes pure rotation about the z axis through a small angle a. Show that its moments of inertia only vary as a if a1. (C2
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z...
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...
7. (10 points) Consider the cube with the eight vertices (+1, +1, +1). Let A, B, and C be the midpoints of the three edges that join with the vertex (1,1,1). (a) What are the coordinates of A, B, and C? (b) What is the equation of the plane through A, B, and C? (c) What is the angle between the plane in (b) and the face x=1 of the cube?
a，b and c，completed processes
134. Idempotent Transformations. Find the matrices of the transformations T which orthogonally project a point (r,y, z) onto the following subspaces of R3. Show by two methods that each transformation is idempotent (i.e., T o T = T). (a) The z-axis. (b) The straight line r-y-2z. (c) The plane 0. + y + z
134. Idempotent Transformations. Find the matrices of the transformations T which orthogonally project a point (r,y, z) onto the following subspaces of...
I have attached the questions and the final solutions. Please do
all of questions 7 and 8
7. Given the line L:x,y,z-2,2,3+1,-1,-3, the plane S 3x-2y+2z-7 and the point A 1,1,1 a) Find parametric equations of the line which contains the point A, intersects the line and which is parallel to the plane b) Find parametric equations of the lne which contains the point A and which intersects the line Lat the&angle a) Show that V" is a subspace of...
Consider the angle shown below with its vertex located at -2,-2). The circle centered at the angle's vertex has a radius 3 units long, and the terminal point is at (0.13, – 4.12). -6 -5 -4 -3 -2 -1 1 2 - 0.13, -4.12) What is the angle's radian measure (assuming that 0 < < 2)? o= Preview Submit License Question 13. Points possible: 1 Unlimited attempts. Message instructor about this question
Question 1 (2+2+5 marks] (a) Find the angle between the vectors y =(4,0,3), v = (0,2,0). (b) Consider the subspace V (a plane) spanned by the vectors y, V. Find an orthonormal basis for the plane. (Hint: you may not need to use the full Gram-Schmidt process.) (c) Find the projection of the vector w=(1,2,3) onto the subspace Vin (b). Hence find w as a sum of two vectors wi+w, where w, is in V and w, is perpendicular to...
Question 10: [8pt total] Consider the line in 3D space (2,5, 2) +t(-6, 4, 2). 10)a) [4pt] Determine vanishing point of the line when centrally projected onto the plane z = 2: Vanishing point: 10)a)ii) (4pt] Graph the central projection of the line onto the plane z = 2. y 6 2 2 8 -6 -4 -2 0 2 8 -2 61
PROBLEM 2 (15 points) (A) Consider the configuration displayed in Fig. la. Two charges of value q are placed at the vertices A and B of an equilateral triangle. Vertex C is at the origin of the coordinate system (0,0,0). Edge AB is in the ry plane and perpendicular to the a axis. Calculate the electric field at vertex C (B) Consider that the triangle is rotated by an angle ф around the z axis, as shown in FigFig. 1b,...
Question 7: [20pt total] The points (-4,4,2), (4,4, 2), (4, -4,4), and (-4, -4,4) form the vertices of a rectangle in 3D space. Q7)a) [12pt] Complete the below table by calculate the central and parallel projections of these points onto the plane z = 1. Point Central projection onto z=1 Parallel projection onto z (-4,4,2) (4,4,2) (4, -4,4) (-4,-4,4) Q7)b) (8pt] Sketch both the centrally projected rectangle and the parallel projected rectangle on the coordinate planes below (be sure to...
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z = 3. (a) Find its moments and products of inertia relative to the origin. (b) The particle undergoes pure rotation about the z axis through a small angle a. Show that its moments of inertia only vary as a if a1. (C2
PROBLEM 1 (10 POINTS) A particle of mass m is located at x = 2, y = 0, z...
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