Give an equation of the plane whose trace in the yz-plane has equation y = 6z, and in the xy-plane has equation y = -8x.

Q: Find an equation for the plane in R³ spanned by the points (1,5,

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Q: Find the equation of the plane in the form z=c+mx+ny containing the line in the xy-plane where x=3,…

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Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

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Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

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Q: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

A: Find an equation for the set of points equidistant from the xy-plane and the yz-plane.

Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

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Q: Find the trace of the plane 8x – 9y + 2z = -11 in the coordinate xz-plane.

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Q: Find an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: Determine the general equation of the plane 2 passing through the point P(-1,4, 5) and parallel to…

A: Follow the procedure given below.

Q: Find the point in the plane 2x − y + 4z = 16 that is closest to the origin.

A: Given:     Plane 2x-y+4z=16 Distance of point P(x1,y1,z1) from plane Ax+By+Cz=D is…

Q: Find parametrizations for the line in which the planes 3r - 6y-2z = 3, and 2x+y-2z = 2 intersect.

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Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

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Q: Find the distance from the point (-2,0,3) to the plane given by the equation 3x+4y 5.

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Q: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

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Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

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Q: Find an equation of the plane containing the line = 3t, y=2-4t, z = 1+ t and parallel to z-axis.…

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Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given    A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: Find an equation of the plane that is parallel to the y-z plane and that passes through the point…

A: NOTE: Refresh your page if you can't see any equations. . the equation of any plane parallel to the…

Q: Find the equation of the plane that contains the point (4, 0, −2) and is perpendicular to the planes…

A: The equation of the plane passing through the point x0, y0, z0 is given as…

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: What is the equation of the plane parallel to 3x + 4y − z = 5 passing through the origin?

A: 3x+4y-z=5

Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

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Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

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Q: Find the equation of the XZ plane.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the distance between the point P(1, -2, 2) and the plane 2x + 3y + 6z - 1 = 0.

A: Formula to find out distance between point and plane is D= |ax+by+cz-d|/√(a^2+b^2+c^2)

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: Find the point in which the line through the origin perpendicular to the plane 2x – y – z = 4 and…

A: We have to find the point in which the line through the origin perpendicular to the plane 2x-y-z = 4…

Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find the trace of the plane in the given coordinate plane. Зх — 9у + 82 %3D7, yz

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

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Q: Find the distance from S(1, 1, 3) to the plane 3x + 2y + 6z = 6.

A: It is given that a point S1, 1, 3 and the equation of the plane 3x+2y+6z=6   Here x1=1, y1=1, z1=3…

Q: Find parametrizations for the line in which the planes 3r- 6y – 2z = 3, and 2x+y-2z = 2 intersect.

A: Given Equation of planes 3x-6y-2z=3 and 2x+y-2z=2

Q: Find an equation of the plane that is parallel to the plane x+ 2y – 10z + 12 = 0 and contains the…

A: The equation of the given plane is  x+2y-10z+12=0 We need to find the equation of plane that is…

Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

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Q: Find an equation of a plane containing the line r=⟨0,−5,−1⟩+t⟨−2,4,−2⟩ which is parallel to the…

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Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: Find parametrizations for the lines in which the planes x - 2y + 4z = 2, x + y - 2z = 5

A: Given the planes :- x - 2y + 4z = 2,  x + y - 2z = 5   The Arbitrarily set z =1 and solve the…

Q: Determine the cartesian equation of the plane having x-intercept of 2, a y-intercept of 5 and a…

A: To find the cartesian equation of the plane

Q: Find the distance between the point Q (3, –2, 4) and the plane 2x – 5y + z = 10 -

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Q: Find the distance from the point B = (1,0, 2) to the plane 2P whose general equation isx + y - z =…

A: Given: equation of plane is x+y-z=1  We know that distanced from the pointx1,y1,z1 to the…

Q: Find the equation of the plane in the form z = c + mx + my containing the line in the xy-plane where…

A: Plane

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.