Consider the infinite geometry R^2, where points are (x, y) ∈R and lines are ax + by + c = 0 with a, b, c ∈R but not both a and b zero at the same time. Show that R^2, as defined above, is an Affine plane.

Q: What is the distance of the origin to the plane through (√3, √3,0), (√3,0, √3) and (0,√3,√3).

A: We have to find the distance of the origin to the plane passing through  and .

Q: A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1.…

A: A set W is defined as consisting of all the planes in R3 that are parallel to the plane x+2y-3z=1.…

Q: 2) = ( (x, y, z) =

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Q: Choose the line which is completely on the plane 2x+3y-4z= 12. Select one: x-1+3t, y= 1+3t, z 2+2t,…

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Q: Prove that if there is a line with n points, then the plane has n^2 points. and Draw a picture.

A: Consider a line with two points, A and B. We can draw a straight line between them. We can choose…

Q: 11. Consider the plane and the line with these equations: 0 = 2x + y -z + 10 a) :. e must b) Find…

A: The line passes through (-4, 2, e) and has direction ratios  3, f, 1 In case (a) the line lies on…

Q: findthe parametríc equatlons for the line through the paint of in tersecti of the lines 4=X=2+ 36 14…

A: first we find intersection point of given line

Q: You are given the following points: A = (11,20, –-18), B= (19,0,3), C =(-7,10,14). Which point is…

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Q: Prove that if there is a line with n points, then the plane has n^2 points. and Draw a picture.

A: Given statement: If a line has n points, then the plane has n2 points. To show: The given statement…

Q: Explain why each set of information does not define a unique plane in three-space. a) x-intercept…

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Q: The distance from (-2,-5,-6) to the yz-plane is (A) -2 (B) 2 (C) (D) -5 (E) 6

A: Use distance between two points

Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

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Q: 2. The plane goes through point A(1,–2,3) and is parallel to the lines x = 2t y = -t +1. Write plane…

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: What is the distance between the point (4,-&, 1) and the plane 5x-z= 2y+5?

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Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

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Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

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