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

Q: Find an equation of the plane. The plane that passes through the point (-3, 1, 2) and contains the…

A: This question is related to planes. We will solve this question by using property of plane

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 an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

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Q: Determine an equation of the plane that contains the point (1, 1, 2) and is parallel to the plane…

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Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

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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: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

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Q: Find a plane through the points P(4,-1,2), Q(6,2,1) and perpendicular to the plane -x+y+z=3

A: Given: Points, P(4, -1, 2) Q(6, 2, 1)

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

A: Given problem:- Find the point of intersection of the line through (1,-3, 1) and (3,-12, 6), and the…

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with .the xy-plane,…

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Q: Let A be the point with coordinates (4, 3, -2) and let B be the point with coordinates (3, 3, -1).…

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

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Q: Find an equation of the plane that is parallel to the plane x + 3y – 8z + 18 = 0 and contains the…

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Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

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: Let A be the point with coordinates (4, 4, 2) and let B be the point with coordinates (3, 4, 3). Let…

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

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

A: Find equation of line and put parametric value of (x,y,z) in plane and solve for x,y and z.

Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

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 general form of the equation of the plane with the given characteristics. Passes through…

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Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

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

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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 plane determined by the intersecting lines.

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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: 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: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

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 an equation for the plane through point (–8, –9, 3) parallel to the plane 6z + 4y – 2z = -87.…

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Q: Find the point of intersection of the line through (1, -5, 1) and (5, -12, 6), and the plane given…

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

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Q: Find a plane containing the point (-4,-7,3) and the line of intersection of the planes - 2x + 7y +…

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Q: Determine the general equation of plane I passing through the point (-4, 3,-1) and parallel to the…

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

A: To Find : Equation of plane passing through (-3,8,-8) that is perpendicular to the plane7x-y+z=2 and…

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

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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: Where does the line through (1, 0, 1) and (3, –3, 4) intersect the plane x + y + z = 6? (x, y, z) =…

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

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Q: Find an equation of the plane that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

Q: Find an equation of the plane parallel to the liner= and containing the points (2, 2,-1) and (1, 0,…

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Q: between the point and the plane. 43. (1,−2, 3); 2x − 2y + z = 4

A: Given: The point is 1,-2, 3 and the equation of the plane is 2x-2y+z=4 To find the distance between…

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

A: This question is based on finding direction cosine using dot product as two perpendicular plane is…

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

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Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: The acute angle of intersection of yz plane and the plane 2x-y+z-4=0 is:

A: Let A1x+B1y+C1z+D1=0 and A2x+B2y+C2z+D2=0 be the equation of two planes aligned to each other at an…

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? (x, y, z)…

A: Useparametric equation of plane to solve

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.