Let L be a line which passes through the point (-7,0,1) and is perpendicular to the plane x + 2y + 7z = 0. Find the z_coordinate of the point of intersection of L and the plane 7x – 7y + 2z = 16

Q: Find the distance from the point (3, 2, 5) to the plane whose general equation is 2x + 3y - z = 0.

A: we have to find the distance from the point (3,2,5) to the plane whose general equation is 2x+3y-z=0…

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

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Q: 2. The plane containing the point (-8, 3, 7) and parallel to the plane given by 4x+8y-2z=45.

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: Locate the point of intersection of the plane 2x + y−z = 0 and the line through (3, 1, 0) that is…

A: Our Aim is to locate the point of intersection of the plane 2x+y-z and theline through (3,1,0) that…

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

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Q: Let p be a plane which contains the point Q(1,2,3) and the intersection line of the planes: 2x+3y-…

A: Concept: 1. The equation of plane passing through the line of intersection of the given planes…

Q: Determine the equation of the plane containing the points (3, 1, 4) and (2,7, 1) and is perpen-…

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Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: Find an equation (in point - nomal form) of the plane containing the point (1.-3,5) and the line…

A: Given:

Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: find the distance between point (-1,1,3) and the plane 5x-5y+3z=25

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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: Find the point-normal form equation of the plane containing the point (1, -3, 5) and the line with…

A: Solution: P(1 , -3 , 5) (2 - x ) = (y+1)/2 = -z/3 = t

Q: Find an equation of the plane whose points are equidistant from (6, -5, 3) and (7,5, 5). 13x + 8z –…

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

A: Distance between the point x1,y1,z1 and the plane ax+vby+cz+d=0is given by-d=ax1+by1+cz1+da2+b2+c2

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: int at which the line ⟨4,−1,−5⟩+t⟨−3,3,2⟩⟨4,−1,−5⟩+t⟨−3,3,2⟩ intersects the plane…

A: Given the line 4,-1,-5+t-3,3,2  intersects the plane -x+y+z=18.

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 the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: The distance from the point K(3, -2, 0) to the xy-plane is Select one: 3 -2

A: Find out the correct option.

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: Find a parametrization for the line SEGMENT between (- 5, 7, 6) and (2, – 6, – 9). |

A: Parameterizing a line segment, which joins the points (x1,y1,z1) and (x2,y2,z2), helps in obtaining…

Q: The line through the point (1, 0, 6) and perpendicular to the plane a + 3y + z = 5

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Q: Find the equation of the plane in xyz-space through the point P = (4, 2, 4) and perpendicular to the…

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Q: Find the distance between (1,-2, - 1)and the plane through the points (1, 2, 3)and (3 , 2, 1)and…

A: Given information: The plane passes through the points (1, 2, 3) and (3 , 2, 1) and perpendicular to…

Q: Find an equation ( in point - nomal form) of the plane containing the point (1.-3, 5) and the line…

A:

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: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7.

A: The distance between a point (x1, y1, z1) and a plane Ax+By+Cz=D is given by…

Q: What is the distance between the point A(1,-1,3) and the plane x + 2y + 2z + 1=0 ?

A: To find The diatance between the point A(1,-1,3) and the given plane

Q: Find the equation of the plane in xyz-space through the point P = (5, 4, 3) and perpendicular to the…

A: NOTE: Refresh your page if you can't see any equations. . the normal vector is  . the given point…

Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

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 (2,-1,3) and the line of intersection of the planes 5x + 7y – 6z =…

A:

Q: Write the equation of the plane passing through point (3, 8, 3)| that is parallel to the xz- plane..

A: Given: A plane passes through (3, 8, 3) and is parallel to the xz-plane. To Find: Equation of plane

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

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Q: Find a plane containing the point (-7,-3,-2) and the line of intersection of the planes 3x – 2y – 3z…

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Q: Find the points of intersection of the line 6. = y+3= z 4 with the plane I+ 3y + 2z – 6 = 0. ОА(-10,…

A: We will solve the following.

Q: Find the point at which the line 7(t) = +t intersects the xy plane. %3D

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Q: Determine the distance between the point (-1, 2, 1) and the plane 2x +14y -5z = 7

A: We know that the distance between a point (x1, y1, z1) and a plane Ax+By+Cz = D is…

Q: Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane…

A:

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

A: To find the distance

Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

A:

Q: What are the projections of the point (3,−2,−7)(3,−2,−7) on the coordinate planes? on the xy plane?…

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

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.