Let A be the point with coordinates (0, -4, -1), let B be the point with coordinates (4, 0, 1), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let II be the plane passing through the three points C,D,E. Suppose that the line 2x - 5 = 2y - 5 = 2z - 5 intersects the plane II at the point P. Write down the x-coordinate of P.

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

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Q: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

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Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given problem:- Find the point of intersection of the line through (1,-3, 1) and (3,-12, 6), and the…

Q: Let A be the point with coordinates (4, 3, -2) and let B be the point with coordinates (3, 3, -1).…

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Q: Find a plane containing the point (-4,-4,6) and the line of intersection of the planes -x + 3y – 2z…

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Q: Determine the general equation of the plane containing the point (1, 2, –1) and the line

A: The given equation of the line- 1-x3=y+23=z-3 It can also be written as follows- x-1-3=y+23=z-31…

Q: Let A be the point with coordinates (3, -7, -2), let B be the point with coordinates (1, -9, -4),…

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Q: Let A be the point with coordinates (1, -3, 2), let B be the point with coordinates (3, -1, -2), let…

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Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find an equation of the plane consisting of all points that are equidistant from (1, 0, -2) and (3,…

A: Let's assume the coordinates of all the points which are equidistant from a points (1,0,-2) and…

Q: Let A be the point with coordinates (4, 4, 2) and let B be the point with coordinates (3, 4, 3). Let…

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Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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Q: Let A be the point with coordinates (3, -7, -4), let B be the point with coordinates (1, -9, -2),…

A: 3D geometry

Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: Let A be the point with coordinates (4, -6, 0), let B be the point with coordinates (2, -8, -4), let…

A: Here we have A be the point with coordinate (4,-6,0) and B(2,-8,-4) and C is the midpoint of AB.

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: Find the equation of a plane consisting of all points that are equidistant from (5,5,-1) and…

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Q: Find an equation of the plane containing the lines given by 1-x = y = z+ 1 2 and * = y – 1 = z - 2…

A: From the given problem:, the plane containing lines are: 1-x2=y=z+1andx+1-2=y-1=z-2 So we can simply…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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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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Q: Find an equation of the plane. The plane that passes through the point (−3, 3, 3) and contains the…

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Q: Find the general quation of plane containing the point P(-1,3,3), and perpendicular to the line…

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Q: Find a full equation of the plane consisting of all points that are equidistant from (0, 1, -1) and…

A: Given two points,  (0, 1, -1) and (-4, 5, -1)  To find the equation of the plane which is…

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

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

A: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

Q: Let A be the point with coordinates (1, 7, 5), let B be the point with coordinates (-1, 5, 1), let C…

A: Given that A be the point with coordinate 1,7,5 and B be the point with coordinate -1,5,1. And C be…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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Q: Find an equation for the plane consisting of all points that are equidistant from the points (-6, 3,…

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

A: C is the mid-point of AB. Therefore, C=-1+12,1+32,1+12=0,2,1 a→=2j+k for Cb→=i for Dc→=j for E…

Q: Let A be the point with coordinates (2, 6, 1), let B be the point with coordinates (-2, 2, 3), let C…

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Q: Find a plane containing the point (5,8,8) and the line of intersection of the planes -4x 4y+ 6z = 74…

A: We have to find the equation of plane containing the points 5,8,8 and the line of intersection of…

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…

Q: Let A be the point with coordinates (4, 4, 3), let B be the point with coordinates (2, 2, 3), let C…

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Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

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Q: Let A be the point with coordinates (3,3,3), let B be the point with coordinates (1,0,0), and let C…

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Q: Determine the way in which the line [x, y, z] = [2, −3, 0] + k[−1, 3, −1] intersects the plane [x,…

A: Here given as x, y, z=2, -3, 0+k-1, 3, -1⇒x=2-k⇒y=-3+3k⇒z=-k .......1 Thus the equation of the line,…

Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

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Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Let A be the point with coordinates (0, 0, 1), let B be the point with coordinates (2, 2, 1), let C…

A: Given: - A be the point with coordinates (0, 0, 1),  B be the point with coordinates (2, 2, 1), C be…

Q: Which of the points A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) is closest to the yz-plane? Which…

A: Given- A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) To do- 1.Which of the points A(−4, 0, −1), B(3, 1,…

Q: Let A be the point with coordinates (4, -4, -1), let B be the point with coordinates (1, -8, -1),…

A: Let A be the point with coordinates (4, -4, -1), let B be the point with coordinates (1, -8, -1),…

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

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Q: 4.) a. Find the point of intersection of the line through (1,-5,1) and (5,-12,6), and the plane…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane

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

A: We will use equation of plane r⇀.n⇀=a⇀.n⇀ Where a→ is a point on the plane and n⇀ is perpendicular…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.