Consider the point. (4, 5, 6) What is the projection of the point on the xy-plane? (х, у, 2) 3D (| 4, 5, 0 What is the projection of the point on the yz-plane? (х, у, 2) %3D (| 4, 5, 6 What is the projection of the point on the xz-plane? (х, у, 2) %3D (| 5, 6, 0

Q: Which of the points A(9, 0, 3), B(6, 5, 6), and C(2, 9, 2) is closest to the yz-plane? Which point…

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Q: Find the distance from the point to the given plane. (1, -4, 6), 3x + 2y + 6z = 5

A: Given:   3x + 2y + 6z = 5     Point: ( 1 , -4 , 6 )

Q: Find the equation of the plane passing through the points P1 (1, 2, ─1), P2 (2, 3, 1) and P3 (3,…

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Q: Find the equation of the plane that contains points Pi(-2,1,4), Р2(1,0,4) and orthogonal to plane…

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Q: 4. What is the equation of the plane through (-1,-1,0) parallel to the plane x + 2y+ 3z 9? (a) x -…

A: To find the equation of a plane through (-1,-1,0) parallel to the plane x+2y+3z=9

Q: You are given the following points: A=(−9,−11,19), B=(20,0,−4),C=(10,−11,−23). Which point is…

A: We need to find distance.

Q: Find a plane through the points P(4,-1,2), Q(6,2,1) and perpendicular to the plane -x+y+z=3

A: Given: Points, P(4, -1, 2) Q(6, 2, 1)

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given  P1 = (10,-8,5) From equation we have point passing through line and parallel vector

Q: Find an equation of the plane. the plane that passes through the point (1, 5, 1) and is…

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Q: 3) Find an equation of the plane whose points are equidistance from the point (2, - 1,1) to the…

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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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: Find the equation of the plane containing the points (1,1,−2),(1,2,1),(−1,2,−2)

A: The equation of plane containing the points 1,1,-2, 1,2,1, and -1,2,-2 is to be evaluated.

Q: Find an equation of the plane. The plane through the points  (3, −1, 2), (8, 4, 5), and (−2, −2, −4)

A: Equation of a plane passing through (x1,y1,z1) , (x2,y2,z2) , (x3,y3,z3) is given by:

Q: Find a plane containing the point (1, 3, 3) and the line of intersection of the planes - 2x - 3y -…

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Q: Find an equation of the plane. The plane through the origin and the points  (3, −3, 7) and (8, 4,…

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Q: 19. The plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) Answer + -4x + 3y + z = -14

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Q: Determine the equation of the plane containing the points: P (1, 2, -3), Q (2, 3, 1) and R (0, -2,…

A: Vector equation of a plane passing through three points with position vector P→,Q→,R→is given by…

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

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Q: Find an equation of the plane. The plane through the point (6, −8, −8) and parallel to the plane…

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Q: 4. Find an equation of the plane that passes through the points P(1,3,2), Q(3,–1,6), and R(5,2,0).…

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

Q: Find the distance from the point (-2, 1, 4) to the plane z = -1

A: Given, plane z=-1 and the point (-2,1,4)we have to find the distance from the given point to the…

Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

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Q: Consider the point. (2, 4, 5) What is the projection of the point on the xy-plane? (х, у. 2) - What…

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Q: Find the equation of the plane passing through (2, 0, 1) and (-1, 2, 0) and perpendicular to the…

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Q: Find an equation of the plane. The plane through the points (0, 6, 6), (6, 0, 6), and (6, 6, 0)

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Q: Find an equation of a plane containing the three points (2, 0, 5), (6, 2, 8), (6, 3, 10) in which…

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Q: Find an equation of the plane. The plane through the points  (2, −1, 3), (6, 4, 6), and (−3, −3,…

A: Let the given points are - A=(2,-1,3) B=(6,4,6) And C= (-3,-3,-3)

Q: Find an equation of the plane. The plane through the points (4, 1, 4), (5, −8, 6), and (−4, −5, 1)

A: ivenThe plane through the points(4, 1, 4) , (5, -8, 6) and (-4, -5, 1)we have to find the equation…

Q: an equation for the plane consisting of all points that are equidistant from the points (-6, 4, 3)…

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Q: 4. Find the equation and sketch the graph of a plane that is parallel to the yz-coordinate plane and…

A: We know that equation of plane parallel to yz-coordinate plane is given by: x=k where k is some…

Q: Give an equation of the plane: (a) (2 points) that contains the point (-2, 1, –3) and perpendicular…

A: GIVEN the plane that contains the points (-2,1,-3) and perpendicular to a line which is passing…

Q: The plane passes through the points (4, 3, 1) and (4, 1, -6) and is perpendicular to the plane 8x +…

A: SOLUTION-

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

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Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: 2- Find un equation 6f the Plane containing the Points (0,0, 2 ), o (2,q!) (-2,3,3).

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Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: 3 Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: The given equation of lines are  x = - 2, y = 4 +2t z = - 3 + t

Q: Find an equation of the plane: The plane through the points (2, 1, 2), (3, −8, 6), and (−2, −3, 1)

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Q: Write the equation of the plane. The plane containing the points (6,-3,1), (5,-4,1) and (3,–4,0).

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Q: -. Which coordinate plane is closest to the point (7, 3, 8)? Find an equation of the sphere with…

A: we have to find the coordinate plane that is closest to the point 7,3,8 and also find the equation…

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: What is the equation of the plane containing the points (4,−3,1), (−3,−1,1) and (4,−2,8)? A. 14x…

A: Solve by eq

Q: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4

Q: Find the equation of the plane passing through the points O = (0,0,0), A = (2,2, –4) and B = (-4,0,…

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Q: Consider the point. (3, 5, 6) What is the projection of the point on the xy-plane? (x, y, 2) = What…

A: given point is (3,5,6) find the projection on xy, yz , zx planes  also find the length of diagonal…

Q: The equation of the plane containing the points (4, – 3,1), (-3,–1,1) and (4, –2,8) is:

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.