a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2 . (without using analytical geometry)

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: .Find the equation and sketch the plane that contains the points (2, 6, 1), (-4, 9, -1) and (4, 3,…

A: Equation of plane is 3x+2y+6z = 12

Q: Show that the following sets of points are collinear and find the equation of the line L containing…

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Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: Prove that the point (1,11),(2,15), and (-3,-5) are collinear and find the equation of the straight…

A: Let the given points be A (1,11), B (2,15), and C (-3,-5). Evaluate the slope of the line AB as…

Q: Find x and y if (2, 5) is the midpoint of points (x, y) and (-5, 6). b. Find the point (0, y) that…

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Q: Plot the following sets of points in a Cartesian plan given set of points consecutively to form a…

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Q: Three or more points are collinear when they all lie on the same line. Use the steps below to…

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Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: iven the points A(2,6,0) and B(3,5,6) determine the point of intersection of this line to x-z plane.

A: Given points are A(2,6,0) and B(3,5,6) The line joining points (x1, y1, z1) and (x2, y2, z2) have…

Q: Let A:(-1, 1, –1), B:(2,0, 2), C:(4, 1, –3), and D:(-3, 1, 10) be points in R. (a) Find the angles…

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

Q: Here let A, B, C, and D be four distinct points in the plane. Now supposedly that no three of them…

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Q: You are given the following points: A=(−4,20,16)A=(−4,20,16), B=(20,0,7)B=(20,0,7),…

A: Given- (x,y,z) coordinates of three points :A =(-4,20,16) B=(20,0,7) C=(8,-15,-19) to find- closest…

Q: Find the equation of the plane that passes through (3,4,-1) and contains the line of intersection of…

A: To work out the equation of the required plane satisfying the given geometric conditions

Q: 4. The points (-3; 4) and (6; -2) are marked on a xy-plane. Which statement about the line through…

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Q: i) x² + 25 y² – 4x + 100y +4 = 0 - ii) x² – y2 – 6x = 0.

A: i) Given equation, x2+25y2-4x+100y+4=0 Now…

Q: x = 1 + 2t, y = 4t, z = 23t; x+2yz + 1 = 0

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Q: how that the lines x- 7y – 22 =0, 3x+4y +9 = 0 and 7x + y – 54 = 0 form a right angled osceles…

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Q: Given are two points [1,3] and (6, –1] in the plane. Which equation of the form a ·z + b•y+c=0…

A: (y-y1)/(y2 -y1) = (x-x1)/(x2-x1) (x1,y1 ) = (1,3) (x2,y2 ) =(6,-1) (y-3)/(-1-3) = (x-1)/(6-1)…