In Exercises 21-24, find an equation of the plane passing through the threepoints given.24. P = (2, 0, 0), Q = (0, 4, 0), R = (0, 0, 2)

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 an equation of the plane. the plane through the points (0, 5, 5), (5, 0, 5), and (5, 5, 0)

A: use the equation of plane(formula) for finding  the equation .

Q: Find an equation of the plane through the three points given: = (5,0,0) , Q = (9, 1, 3) , R= (8, 4,…

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Q: Find an equation of the plane passing through the three points given.P = (2, −1, 4), Q = (1, 1, 1),…

A: To find the equation of the plane passing through the three pointsP =x1,y1,z1= (2, −1, 4), Q…

Q: Find an equation of the plane. The plane through the point (8, -8, -8) and parallel to the plane 5x…

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Q: Find an equation for the plane through the points (3, 2, 3), (–1,2,0), (1,0, –1). The plane is

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Q: 8. Find the equation of the plane that contains the points P,(3,1,–2), P2(0, –2, 1), and P3(-2, –5,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, 2, 3), 2x + y + 2z = 4 40.…

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Q: At what point does the plane through A = (1,0, 0), B = (2,1, 1), and C = (-1,3, 4) cross the y axis?…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 2, 2) and contains the…

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Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: 10. Find an equation of the plane that passes through the points (x, y, z) = (1, 2, −1), (x, y, z) =…

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

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Q: Find an equation of the plane. The plane through the point (5, -3, -3) and parallel to the plane 4x…

A: We can use the concept of plane in order to solve the given problem.

Q: 4- Find an equation of the plane that passes through the given points (-2, 1, 1), (0, 2, 3), and (1,…

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Q: a) Find the point of intersection between the lines x = 2t, y =t+ 2, z = 3t – 1 x = 5k – 2, y = k+…

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Q: 2. Find the equation of the plane through the points (1, -3,2), (3,0,– 1), and (0,5,5).

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Q: Find the point on the plane −2 x+y−z =−9 that is closest to the point (3,−2,2) .

A: We have to find a point on the plane closest to another point.

Q: Exercises 57–60, find the point in which the line meets the plane. 57. x = 1 - t, y = 3t, z = 1 + t;…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the equation for the plane through the points Po(-3,- 2, – 4), Qo(2,1,3), and Ro(3, - 2, – 5).…

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Q: 3. Find an equation of the plane passing through the points (-1,2,0), (2, 3, 6), and (-1, 5, 2).

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Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13…

A: Given, (2, -3, 4), x + 2y + 2z = 13.

Q: Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0)

A: Given:Plane passing through points 0,7,7 7,0,7 and 7,7,0To find; equation plane passing through…

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x y+z=2…

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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: 5 Find the equation of the plane passing through the points A(1, 2, –3), В(2, 1, 4), С(3,0, 1).

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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 the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

A: Given: points (0,1,3), (2,2,2), (3,2,1) Find: equation of the plane containing given points

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x - y + z…

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

Q: In Exercises 41-44, find the intersection of the line and the plane.42. 2x + y = 3, r(t) = (2, -1,…

A: Given: To find the intersection of the line and the plane.2 x + y = 3,  r(t) = (2, -1, -1) + t (1,2,…

Q: Z= (a) What is the equation of the plane passing through the points (2, 0, 0), (0, 2, 0), and (0, 0,…

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Q: Find an equation of the plane containing the points (0,0, 2), (2, 4, 1) and (–2, 3, 3)

A: Given:      Points 0,0,2, 2,4,1 , -2,3,3 Recall that we can generally write the equation for a plane…

Q: Find an equation of the plane containing the points (0,0, 2), (2, 4, 1) and (–2, 3, 3).

A: Equation of a plane containing 3 points is x-x1y-y1z-z1x2-x1y2-y1z2-z1x3-x1y3-y1z3-z1=0

Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

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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: How to find an equation of a plane through a specific point such as (3,0,3)?

A: There can be infinitely many planes passing through one point and hence you can not find an equation…

Q: Find an equation of the plane passing through the points.(0, 0, 0), (1, −1, 0), (0, 1, −1)

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Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

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Q: In Exercises 33 and 34, find the distance from the point to the plane.33. (6, 0, -6), x - y = 434.…

A: We have given; 33. (6, 0, -6), x - y = 434. (3, 0, 10), 2x + 3y + z = 2

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 the plane through (-1,-1,0) parallel to the plane x+2y+3z=9

Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x-y + z =…

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Q: In Exercises 41-44, find the intersection of the line and the plane.43. z = 12, r(t) = t (-6, 9, 36)

A: the line we get  r(t) = (-6t, 9t, 36t) x = -6t y = 9t z = 36t

Q: Find an equation of the plane. The plane through the points (0, 2, 2), (2, 0, 2), and (2, 2, 0)

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Q: 3. Find the equation of the plane through (-3, 8, -8) that is perpendicular to the plane 7x– y + z =…

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

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: 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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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.