1. Calculate the below questions using basic properties of projective geometry: a. Suppose there are two points on projective plane P?, A(2,5) and B(4,0). Find the line through those points using the homogeneous representation! b. Suppose there are two lines on projective plane P?, y = -2 and y = -2. Find the intersection of the two lines using the homogeneous representation! c. Prove that the point: C(1,1) on projective plane P2 lies on the line: x – y = 0 using the homogeneous representation!

Q: 2. Given the points A(2,2,1) and B(9,3,6) and the plane K: 2x+6y+6z-9=0 Define: a. do points A and B…

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Q: x²+x-12 +12, determine the intercepts, the equations of all asymptotes, x²-4 Given the function:…

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Q: 5. Find the point of intersection of the given plane and line. Plane: 2x - y+3z=7 Line: x=-1+t y…

A: We have to find  point of intersection .

Q: Explain why or why not Determine whether the following state- ments are true and give an explanation…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: 1. Find the equation of the plane that contains the following points. (2, –1, 4), (3, 2,0), and…

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Q: 8. Let P(1,2,3), Q(1,-1,-2), and R(0,0,0) be the three points in R³ a. Find an equation of the plane…

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Q: ln the ry-plane, the point P (2, 3) is first reflected across the x-axis to point Q, and then Q is…

A: Given point (2,3)   Reflection of (x,y) to x axis gives (x,-y)

Q: 1. Do the following equations describe lines (L) or planes (P)? a) [x, y] = [1, 1] + s[2, 3] b) [x,…

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Q: by the equations { L₁ : X Y Let L₁ and L2 be lines in a 3-dimensional space given { = = Z = 3 + 2t…

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Q: 2. Let P be a point not on the plane that passes through the points Q, R, and S. a. Show that the…

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Q: 2. Given the planes P: 2(x-1)-(y+1)-2(z-2)=0, P₂: 4x-2y+5z=3\ and the point Q: (-2,7,4). a.…

A: Given: There are two planes P1 and P2. P1:2x-1-y+1-2z-2=0 andP2:4x-2y+5Z=3 Also, a point Q(-2, 7, 4)…