Count all the incidences in S4, a four-dimensional projective space of order q. That is, determine the number of (a) points and hyperplanes in S4; (b) lines and planes in S4; (c) points in each of a line, a plane and a hyperplane; (d) lines in each of a plane and a hyperplane; (e) lines through a point; (f) planes in a hyperplane;

Q: If two planes intersect, then _____.

A: Intersection of two planes is given by,

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Q: 8. Sketch the graph of the plane given by *P. Note: a potential answer is on the next page. b. а.…

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Q: a) What is the equation of the line parallel to LM passing through N with point(X1,Y1). b) Show…

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Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: Equation: Answer:

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Q: 1. (a) Define what a linear subset of a projective space is.

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Q: Suppose that an isometry of a plane leaves three noncollinear pointsfixed. Which isometry is it?

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Q: 1. Give a geometric description of the set of points in space whose coordinates satisfy the given…

A: Given: Let us consider the given set of points, a) x=-1, z=0 b) x2+y2+z2=25, y=-4 c) x2+y2=4, z=-2

Q: 19. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) Answer + -4x + 3y + z = -14

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Q: can a given line be in a two planes?in ten planes?

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Q: a. Draw the affine plane, AG(2, 3). b. How many points are in AG(2, 3)? How many lines? How many…

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Q: 1. Determine the intersection (if any) of the following planes. Show your work clearly and be sure…

A: (a).The given planes are:π1:  2x+y-3z=5π2:  3x+4y+3z=6

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Q: 1. The points P, (1,2,3), P₂ (2, 1, 2), P, (3, 0, 1), P4 (5, 2,7) are the vertices of a plane…

A: Step 1: Step 2: Step 3: Step 4:

Q: (1) There are 12 points A, B, ... in a given plane, no three on the same line. The number of…

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