Find a line passing through (−2, 5, −3) and perpendicular to the plane 2x − 3y + 4z + 7 = 0.

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

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Q: Solve for the distance from the point (-5, 4, 5) to the plane −x+4y−5z=4.

A: Given Plane: -x+4y-5z=4 and Point: (-5,4,5)

Q: Find equation of the plane that contains the lines L1:x = 3 + 5t, y = 6+ 2t, z = 6 + 3t and L2: x =…

A: Equation of plane which passes through L1 is ax-3+by-6+cz-6=0 where 5a+2b+3c=0.

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

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Q: Find the equation of the plane containing the point (- 7, – 8, 0) and parallel to the plane 6x + 8y…

A: To find equation of a plane we use Concept of Direction Ratio of the given parallel plane.

Q: Find the distance from (−2, 4, 5) to the plane 2x + 6y − 3z = 10.

A: we know that distanced of pointx1,y1,z1 from the plane ax+by+cz=d is given by…

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

A: The vector normal to the plane ax+by+cz=d is ai^+bj^+ck^ . The plane parallel to this plane has the…

Q: Find the distance between the parallel planes: 3x - 4y + z = 12 6x - 8y + 2z = 2

A: Given, The equation of planes  3x - 4y + z = 12 6x - 8y + 2z = 2   We have to find the distance…

Q: find the equation of the plane passing through(1,0,-1)&(-1,2,1) and parallel to the line of…

A: To determine: The equation of the plane passing through the points (1, 0, -1) and (-1, 2, 1) and…

Q: Find an equation of the plane that passes through the point (1, 6, −4) and contains the line:

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Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: Find an equation of the plane that is parallel to the plane x + 7y – 2z + 20 = 0 and contains the…

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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 the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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Q: Find the equation of the line that contains the point (1,–1, 2) and is perpendicular to the plane 2x…

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Q: Find the point where the line x=8+2t, y3-2t,z=1+t intersects the plane 3x+2y+6z36.

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Q: ) Find the equation of line of intersection of the following planes 3x – 4y + 4z – 29 = 0 , 6x – 8y…

A: Explanation of the solution is given below...

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

A: We have to find the intersection of the plane 2x+y=3 and the straight line r(t)=2,-1,-1+t1,2,-4

Q: Find the linear equation of the plane through the point (1, 7, 6) and parallel to the plane x + 3y +…

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Q: What is the real number a that makes the line 2 -1 y-12 z-7 a -2 3 parallel to the plane z -y - 2z=…

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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: Find all planes in R^3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.

A: To find all planes in ℝ3 whose intersection with the xz-plane is the line with equation 3x + 2z = 5.…

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

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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 (-2, 2, 1) + t(5, –4, 3) intersects the plane -4x – 4y + z = -5.

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Q: Find the distance between the parallel planes P1: 2x – y + 2z +6=0 and P2:6x- 3y+6z- 18 = 0

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Q: Find the equation of the plane that contains the line 2 5-x 2+y – 5 – z, and the 3 point P( 0,5,2).…

A: We have to find the equation of the plane that contains the line and the point.

Q: Find the point at which the line (-4, 1,1) + t(2, -5, 4) intersects the plane -5x+ 3y – 3z = -54.

A: the given line is  xyz=-411+t2-54 xyz=-411+2t-5t4t xyz=-4+2t1-5t1+4t

Q: Find equation of the line passing through the point (4, 2, 6) and parallel to the line of the…

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Q: Find the distance between the parallel planes P1: 2x – y+2z + 6 = 0 and P2: 6x - 3y+ 6z – 18 = 0 3y…

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Q: Find an equation of the plane that passes through the point (-1, 4, 2) and contains the line of the…

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Q: Find the point at which the line (-4, –5, 2) + t(-4, 3, –5) intersects the plane 2x + 5y + 4z = -6

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Q: Solve for the linear equation of the plane through the point (1,9,10)(1,9,10) and parallel to the…

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Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z=x+ y.

A: Given, Plane is passing through the point (3, -2, 8) and Parallel to the plane z=x+y    Equation of…

Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: Find the point at which the line (-3, -4,-2)+t(5, -4,-2) intersects the plane -5x +3y+z= -155.

A: Given: line equation: -3,-4,-2 +t (5,-4,-2) Then equation of line from parametric equation is given…

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 equation of the plane through Po (2,-1,-1) and P1(1,2,3) and perpendicular to the plane…

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Q: Find equation of the plane through (1,0,-1).(-1,2, 1) and parallel to the line of intersection of…

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Q: Find a plane containing the point (1,-8,-3) and the line of intersection of the planes - 3x – 8y +…

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Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

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Q: find the equation of the plane passing through (1,0,-1)&(-1,2,1) and parallel to the line of…

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Q: Find the equation of the line of intersection of the planes 2x+y-2z = 1 and x+2y-z = 4.

A: Planes are 3-dimensional spaces, that contains infinite lines. When two non-parallel planes…

Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: Find the equation of the plane that contains the point P(-6, 5, 7) and is perpendicular to the line…

A: Use direction ratios of line to find direction ratios of plane. Then use the point to find equation.…

Q: Find the distance from the point (7,-9,-5) to the plane 3x + 5y = 51.

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Q: Find the equation of the plane through (2,4,-1) and contains the intersection line of the planes…

A: Let's find.

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.