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

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

A:

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

A: