Find the equation of the set of points located three units away from the plane -2х + бу + 3z + 1 %3D0. А) 2х — 6у + 3z — 3 %3D 0 в) — 2х — бу + 3z + 2 %3D 0 or —2х — бу + 3z — 2 %3D 0 C) 2х — 6у + 3z + 10 %3D 0 D) —2x + 6у + 3z— 20 %3 0 оr -2x + 6у + 3z + 22 3D 0 2х — бу + 3z +3 %3D 0 or 2х + бу + 32 —11 %3D 0 or E) None of the above.

Q: Find an equation for the plane that passes through the point (-7, 10, –8), is parallel to the line x…

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Q: Find a line equation through the point P(3,-1,4) and parallel to the line of intersection of the…

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Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 15у — 12z — 2 %3D 0 (a)…

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Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Find the equation of the plane through the point (2,4,3)(2,4,3) that is perpendicular to the line…

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Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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Q: Find an equation of the plane determined by the points P(1,2,3), Q(2,0, 1), and R(0, –-1,1).

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Q: Find the angle of intersection of the plane 2x+3y+5z=−32x+3y+5z=−3 with the plane 3x+2y−1z=0

A: Given: - The plane is, 2x+3y+5x=-3, with the plane 3x+2y-z=0 To find: - The angle of intersection of…

Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: Find the distance between the given parallel planes: (a) 2x - 3y + z = 4 and 4x - 6y + 2z = 3 (b)…

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Q: Find the intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

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Q: Show that the distance between the parallel planes                                          ax + by…

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Q: Find the distance between the given parallel planes. 2x- 2y +z = 10, 4x-4y+2z= 1 4x – 4y+2z = 1 19…

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Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: Find an equation of the plane through (-3, 8, – 7) that is perpendicular to the planes 6x – y +z = 4…

A: We need to find equation of plane.

Q: Determine if the plane given by -x + 2z 10 and the line given by %3D (x = 5, y = 2 -t,z = 10 + 4t)…

A: given plane: -x+2z+10 given line: (5,2-t,10+4t)

Q: Find the distance from the point A(2,4,3) to the plane determined by the three points B(1,4,2),…

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Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Determine the equation of the plane that passes through (2,-4,1) and is perpendicular to the line of…

A: A plane is passing through 2, -4,1 and perpendicular to the line of intersection of the plane  3x -…

Q: find an equation of the plane passing through the three points given.  P = (2, 0, 0), Q = (0, 4, 0),…

A: Equation for plane P is written in vector form as: n.(x,y,z)=d In scalar form equation is written as…

Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

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Q: 3x + 30 (5y 2)° 5z +5 8х — 5 (9y 8) SR = RT mZT AS 4z 8 %S4

A: we will find in next step

Q: Determine if the three planes -x-5y-5z= 2, 4x -5y +4z = 19 and x +5y - z = - 20 have an intersection…

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Q: Find an equation of the plane through (-8, 6, - 6) that is perpendicular to the planes 9x - y + z =…

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Q: Find the intersection of the line r(t) = (2, 1, 3) + t(3, -3, 1) and the plane 4x - 4y - 2z = 6.

A: Given, Line-> r(t) = (2, 1, 3) + t(3, -3, 1) Plane-> 4x - 4y - 2z = 6 ------equation 1

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

A: For solving This question I found direction cosine using dot product as two perpendicular plane is…

Q: Find an equation of the plane through (-2, 8, – 5) that is perpendicular to the planes 2x – y + z =…

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Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

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Q: Find the point at which the line intersects the given plane: 5x = y/2 = z + 2 and 10x - 7y + 3z +…

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Q: The plane equation that has 2.5 units distance to the plane 5x- 2y + 3z = 4 is %3D O a.…

A: Option (d) is correct.

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: What is the equation of the plane containing point (3,0,4) and orthogonal to the line…

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Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

A: Verify that the two planes x − 3y + 4z = 10 , x − 3y + 4z = 6 are parallel and find the distance…

Q: Find the distance between the given parallel planes 4x – 2y+z = 16, 8x – 4y+2z=2 3 a. 3 b. 5, 14 3…

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Q: -6x - Find dA, where Ris the parallelogram enclosed by the lines -3x+y R – 6x – y = 0, – 6x – y = 2,…

A: I have used jacobian to solve the area of above double integral.thanks

Q: Find the point of intersection of the line with equation L: (x,y,z) = (1, - 1,0) + t(1,1,2) and the…

A: To find the intersecting point, we substitute the values of x, y, and z in the equation of plane and…

Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

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Q: Find the distance between the given parallel planes. 2x - 4y + z = 8, 4x - 8y + 2z = 3

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Q: Find the points of intersection of the line x = 3+2t, y =5+7t, z = -3+t, that is, I(t) = 3+2t, 5+7t,…

A: To determine the intersection of the line with the coordinate planes.

Q: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: Find an equation for the plane parallel to the line x = 1 − 2t, y = 2 + 3t z = 1 + 2t and that…

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Q: Find an equation of the plane through (-8, 4, –9) that is perpendicular to the planes 5x – y +z = 1…

A: Solution of question is written in below steps.

Q: Find the equation of the plane through (-6,5,-1) and is parallel to the xy plane

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Q: Find the point at which the line (0, –3, 5) + t(4, –1,2) intersects the plane 4x + 4y – 4z = 0.

A:

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.