Suppose there is a plane in three dimensions created from three coordinate points P(x,y,z), Q(x,y,z), and R(x,y,z). Suppose there is a line in three dimensions created from two coordinate points A(x,y,z) and B(x,y,z). Use a formula or algorithm to detect when the line AB intersects through triangle PQR. When it does, find the intersection point C(x,y,z) that is both on the line AB and inside the triangle PQR. Manual and computer/calculator methods are both welcome.

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: 1. Find an equation of the plane that passes through the points (-1, 3, -3), (4, 1, 2), and (8, 2,…

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Q: Let A be the point with coordinates (1, 9, 5), let B be the point with coordinates (-3, 5, 1), let C…

A: Given coordinates are, A=1,9,5B=-3,5,1 So, the midpoints of AB is C1-32,9+52,5+12=C-1,7,3.

Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: In the projective plane, Z5P2, find the line that contains the points (1,2,1) and (2,1,4).

A: In projective geometry over a finite field, such as , we can find the line that contains two points…

Q: Suppose a plane through three points A(1,-2,4), B(1,-1,6) and  C(2,0,5). Solve the following two…

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Q: 4. Consider the points A(1, 0, 3), B(-1, 5, 2) and C(3, -1, 1). Find the equation of the plane…

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Q: Find the equ. nf line through the Pont (-2,3,4) and Parallel to Planes: 2X+3y +42=5 3X + 4Y+52=6…

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Q: 2. The x- and y-axes divide the coordinate plane into four regions called

A: Given: The x and y axes divide the coordinate plane into four regions

Q: Let A be the point with coordinates (-6, -2, 0), let B be the point with coordinates (0, 4, -2), let…

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A: Given points P1,3,2, Q3,-1,6, R5,2,0

Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

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Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: the

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Q: 4) Find line of intersection for 2 planes.  2x-3y+z=5 -x+2y+3z=2

A: We will solve the problem

Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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Q: Let A be the point with coordinates (0, -2, -3), let B be the point with coordinates (2, 0, 3), let…

A: Equation of plane through three given points is given by…