@/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for the line of intersection (L)of these two planes.

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

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Q: Find an equation of a plane making an angle of π/2 with the plane 3x + y − 4z = 2

A: Here we have to find the equation of plane  making an angle of π/2 with the plane 3x + y − 4z = 2

Q: Find the angles between the planes x + y = 1, 2x + y - 2z = 2

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Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: A line, passing through point (6, 3, 2) and is perpendicular to the yz-plane. Find a point on this…

A: We answer only one question at a time , so we will answer the first question since the exact one…

Q: Find the intersection between the plane  4x−y+5z=18  and the line through the points  (0,0,1)  and…

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Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

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

A: Given: The point (-1, 3, -1) and the plane -1x+2y-5z=1 To find: The distance.

Q: Calculate the distance between the points P = (-7, 0) and N=(-4, -6) in the coordinate plane. Give…

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Q: Find the distance between the point (-1, 1,-1) and the plane 3x - 5y + 2z = 12

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Q: ....... Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane…

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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 angle between the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5.

A: Given equations of the planes3x-6y-2z=15 and2x+y-2z=5we have to find the angle betweenthem θ

Q: Find the distance from point P(2, 7, -6) to the plane of equation 5x - y + 4z - 8 = 0

A: We have to find distance

Q: Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

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

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Q: Locate the point of intersection of the plane 2x + y - z = 0 and the line through (4,2,0) that is…

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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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: Equation of the plane passing through the point (4, –2, –1) and parallel to yz-plane is

A: To find the equation of the plane passing through the point 4, -2, -1 and parallel to yz-plane.

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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Q: Find the angles between the planes 2 x + 2 y + 2 z = 3 and 2 x – 2 y-z 5

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Q: Line 1: 1 - y = Z – 8 2 х — 3 4 Line 2: x=-2t y=2+2t z=6+2t 1.If the given lines intersect at a…

A: To find the given questions when two lines Line1 and Line2 are given :-

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y - z = -2? (x, y, z)…

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Q: Find the distance from the point (-5, –13,6) to the plane –9x + 3y – 8z = -67. Distance is ...

A: Given:            point a(-5,-13,6)=(x0,y0,z0)            plane equation is -9x+3y-8z+67=0we know…

Q: Where does the line through (-3, 1, 0) and (−1, 3, 8) intersect the plane 2x + y − z = -2? (x, y, z)…

A: Given the points (-3,1,0) and (-1,3,8) and the plane 2x+y-z=-2

Q: 3. Through the point (4, -5, 20) and perpendicular to the plane x + 3y – 6z - 8 = 0.

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Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given the point (1,-3,1) and (3,-12,6) and the plane x-y+z=6

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

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Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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

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Q: Find the angle between two planes -3/2x- 6y+ z= 4 and 2x−y−1/2z= 7 , also find an equation for the…

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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: Calculate the distance between the points H=(-2, -3) and N=(-8, 2) in the coordinate plane. Give an…

A: We know that the distance between the points x1, y1 and x2, y2 is given by x2-x12 + y2-y12

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: Find angle between two planes given by 2x + y – z = 29 and 3x + y + 2z = 6. %3|

A: we have to find the angle between the two planes given by 2x+y-z=29 and 3x+y+2z=6. the equations of…

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

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Q: Give the coordinates of Z" after Triangle XYZ with vertices X(-6,4), Y(0,6), Z(-4,2) is reflected…

A: Since you have posted multiple questions, we will solve only first question for you. To get…

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: The distance from the point S(-7, 8, -4) to the plane 10x+2y+11z=2. 20 3 8 15 8 225

A: The equation of the plane is  10x+2y+11z = 2 The point is S-7,8,-4 To evaluate : The distance from…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find the equation of line and then find its intersection with the plane

Q: Where does the line through (-3, 1, 0) and (-1, 7, 4) intersect the plane 2x + y -z = -2?

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Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

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Q: Find the distance from the point (-1,4,5) to the plane 3x+2y-4z=5?

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

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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.