linear algebra: Consider the cube with the eight vertices (±1, ±1, ±1). Let A, B, and...
linear algebra:
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?
Homework Answers
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linear algebra:
Consider the cube with the eight vertices (±1, ±1, ±1). Let A, B,
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Consider the unit cube with vertices (corner points) (0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (...
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Please show work, thanks!
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question 1 and 2 please, thank
you.
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linear algebra
Remember we were able to express rotations and reflections, which are geometric transformations, using a linear transformation T, the coef- ficient matrix corresponding to the geometric transformation (r. y) (r', ) (a) What problem do you encounter with translations (r. y) (r+ h.y+k)? To handle this problem, We let the vector (x, y1 ) in R2 correspond to the vector (x1, y1, 1), and conversely. (In effect, we're projecting the :xy-plane onto the plane 1) introduce homogeneous coordinates....
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?
Consider the unit cube with vertices (corner points) (0, 0, 0),
(0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1),
(1, 1, 1). Let S be the boundary of the cube minus (i.e. not
including) the bottom square (the side which lies in the xy plane).
Orient S with the normal which points out of the cube. Let F =
<− y , x , y^2e^x . Evaluate (curl F) ·...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
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Please show work, thanks!
Let the deformation where ai, a2, and a3 are constants be applied to the unit cube of material shown in the sketch. Determine (a) the deformed length l of diagonal OC, (b) the angle between edges OA and OG after deformation, (c) the conditions which the constants must satisfy for the deformation to be possible (1) the material is incompressible, (2) the angle between elements OC and OB is to remain unchanged. x,,x, X2 , X2...
Consider the rotational symmetry group G of the cube Let X be the set of edges of the cube, and let xe X be the edge between faces A and E (see picture). G acts on X in the obvious way. Describe the stabilizer Stabg(x) and the orbit Orbg(x). By using the orbit-stabilizer theorem, deduce G.
question 1 and 2 please, thank
you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
linear algebra
Remember we were able to express rotations and reflections, which are geometric transformations, using a linear transformation T, the coef- ficient matrix corresponding to the geometric transformation (r. y) (r', ) (a) What problem do you encounter with translations (r. y) (r+ h.y+k)? To handle this problem, We let the vector (x, y1 ) in R2 correspond to the vector (x1, y1, 1), and conversely. (In effect, we're projecting the :xy-plane onto the plane 1) introduce homogeneous coordinates....
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