Let "r" be the line determined by the intersection of the planes x+y-z= 0 and 2x-y+3z-1=0.Find the equation of the plane that passes through the point A(1.0,-1) that contains the line " r"

Q: Find an equation of the plane containing the point P (1, -7,1) and the line r (t ) = .

A: Given: The point P (1, -7,1) and the line r (t ) = <3 − 2t, 4t, 7> . So,             x = 3 −…

Q: Find the point, P, at which the line intersects the plane. x = - 2+ 2t, y = - 3+ 8t, z= - 10 + 4t;…

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Q: Write the equation of a plane that intersects at the coordinate axes OX and OY segments 2 and -17…

A: Given that: Intercepts of  a plane with coordinate axes: OX=2 and OY=-17and Plane passes through…

Q: The plane perpendicular to the y-axis and passing through the point (9, -10, -7)   a) 9x - 7z = 0…

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Q: (a) Find the point at which the given lines intersect. r= (1,3, 0) + t(3, -3, 3) r = (4, 0, 3) +…

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Q: 2. Find a plane perpendicular to the planes x + y - 3z = 0 and x - 2y-2z = -1. Your answer

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Q: Line Li: 0.5C1- X)= 2 = 0.5z intersects the plane defined by B(2,237), C Cl,o, 12) at point P. Find…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

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Q: Find the linear equation of the plane through the point (2,3,6) and parallel to the plane…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

A: For the solution follow the next steps.

Q: Find the equation for the plane through the points Po(3,4,2), Q,(-1,0, – 1), and R,(-1,-3,0). Using…

A: we have to find the equation of a plane passing through the points P0(3,4,2),Q0(-1,0,-1) and…

Q: identify and sketch the set of points in the plane satisfying x2 + 2x - y = 3

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Q: . A-line perpendicular to the plane 3x-4y+z=1 passes through the point A(-1,3,2). Find the…

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Q: Give an equation of the plane determined by the intersecting lines L1 and L2 L1 : x = 2t y = 4 – t z…

A: The equation of two lines is given as follows: L1: x=2t, y=4-t, z=3+t L2: x=2+s, y=-3+2s, z=s The…

Q: Find an equation of the plane with the given characteristics. The plane passes through the point…

A: Given problem:- Find an equation of the plane with the given characteristics. The plane passes…

Q: Find the plane containing the intersecting lines: L1: x = -1 + t, y = 2 + t, z = 1 - t; -∞< t < ∞…

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Q: Lienar Algebra Let the line pass through the points A(1, 0, 1) and B(0, 1, 1). Calculate the…

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Q: Find the point on the plane x−3 y+3 z =−8 that is closest to the point (−2,−2,0) .

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Q: x-2 Show that the lines y+3 z+4 and 4 X-11 y-9 z-11 1 intersect %3D %3D %3D %3D

A: NOTE: Refresh your page if you can't see any equations. . the first line is  write the above line…

Q: 24. Let A = (2,1) and B = (-1, –2) be two points on the plane. Write the equation of the line which…

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Q: Coordinates of point which partitions a directed line segment AB at the ratio of a:b from A(xyı) to…

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Q: Linear Algebra Let "r" be the line determined by the intersection of the planes x+yz= 0 and…

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Q: QI/ Determine whether the two planes are parallel or intersecting. Find their line of intersection…

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Q: Determine if each statement is true or false, and explain your response An equation of the plane…

A: Answer and explanation is given below........

Q: The line = (2, -1, -2) + s(1, 1, -2), sER, intersects the xz-plane at point P and the xy-plane at…

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Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: Show that planes 2x- y + z = 0 and x+2y-z = 1 intersect according to a straight r.

A: General Equation of a Plane: A plane can be represented by an equation of first degree in such as…

Q: Algebra Linear Find the equation of the line that passes through point A(1, 0, 1) and is parallel…

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Q: Find the point, P, at which the line intersects the plane. x= 8- 2t, y = - 10+ 2t, z = 9– 3t; 10x -…

A: Substitute the point of the line in the equation of the plane and solve for t

Q: Find an equation of the plane. The plane through the points (0, 7, 7), (7, 0, 7), and (7, 7, 0)

A: Given:Plane passing through points 0,7,7 7,0,7 and 7,7,0To find; equation plane passing through…

Q: Linear Algebra  Determine the line r that passes through points A(4, 0, 1) and B(5, 1, 3). Then…

A: we have to determine the equation of a line r passing through points A(4,0,1) and B(5,1,3). then we…

Q: Find the equation for the plane through the points Po(-2, - 3, – 2), Q,(4,0, – 4), and Ro(3, – 3, –…

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Q: Find the coordinates of the point. The point is located nine units in front of the yz-plane, eight…

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Q: (a) Find the point at which the given lines intersect. r = (1, 3, 0) + t(3, -3, 2) r = (4, 0, 2) +…

A: Introduction: When a line in three dimensional Euclidean geometry passes through a point with a…

Q: Linear Algebra Let α be the plane that passes through the origin and is perpendicular to the line…

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Q: nd an equation of the plane. The plane through the points (0, 4, 4), (4, 0, 4), and (4, 4, 0)

A: Given A0,4,4 B4,0,4 C4,4,0

Q: a. Find an equation of the plane that passes through (3, 2, -1) and contains the line l(t)= (-t, 2,…

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Q: 22. a) Determine the equation of the line of intersection of planes 1 and 2. Express your answer in…

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Q: Find the coordinates of the point. The point is located in the yz-plane, seven units to the right…

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Q: Three intersecting planes Describe the set of all points (if any) at which all three planes x + 3z =…

A: Consider the planes, The objective is to describe the set of all points at which all above three…

Q: 1) Find the equations of the line that passes through point Q(1, 2, 1) and is perpendicular to the…

A: Given plane is Equation of a line is

Q: Rectangle WXY Z has vertices located at W(-6, 4), X(-6, –1), Y (2, –1), and Z(2, 4) on a coordinate…

A: Vertices of rectangle WXYZ are W-6, 4,  X-6, -1, Y2, -1, and Z2, 4.

Q: Find an equation of the plane. The plane through the points  (0, 9, 9), (9, 0, 9), and (9, 9, 0)

A: A per our guidelines we are instructed to answer one question at a time. Submit the second question…

Q: Use the equation quadratic 4x²+9y²+18z²=72 to obtain the trace equation in plane z= √2 . Determine…

A: Substitute the value of z in the equation, 4x2+9y2+18z2=72 and simplify to obtain the equation of…

Q: Find an equation of the plane. The plane that passes through the line of intersection of the planes…

A: Given query is to find the equation of the indicated plane.

Q: Ноше work Find an equation of plane through the points pl (-1, 1, 1) and point intersection of the…

A: Here we have to find the equation of the plane passing through the point P1(-1,1,1) and point of…

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

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.