Find an equation of the plane through the three points given: P = (0, 1, 0), Q = (-3, 4, – 1), R = (2, –2, – 1) = -5

Q: Find the equation of the plane through (1,2,3) and parallel to the plane: x+y=-2-z

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Q: Determine a cartesian equation of the plane through the points  P1 =(1,2,-1), P2=(0,2,-3) and…

A: Determine a cartesian equation of the plane through the points  P1 (1,2,-1), P2(0,2,-3) and parallel…

Q: Find the equation of the plane through (1,-4,2) and per pendicular to each of the planes 2x t 5y -2…

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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 an equation of the plane through the three points given: P = (3,0,0), Q = (5, 1, 2), R = (7, 2,…

A: Let the equation of the plane passing through three points be  Ax+By+Cz+D=0 This plane passes…

Q: Find the general equation of the plane π  that passes through the origin and is perpendicular to the…

A: Suppose a plane passing through the points x1,y1,z1 and a vector perpendicular to the plane is…

Q: Find an equation of the plane through the three points given: P = (0,0, 5), Q = (-4, 1, 3), R = (-3,…

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Q: Find an equation of the plane determined by the points P(0,0,0), Q(-1,2,4), and R(2,1,3)

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Q: Write the equation of the plane that contains the point P(1, 3, 5) and the line L: x = 4t, y = 6 +…

A: It can be solved using properties of plane.

Q: Find the equation of a plane passing through ?(2,1,3), ?(3, −1,5), and ?(1,2, −3)

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Q: find an equation of the plane passing through the three points given.  P = (2, 0, 0), Q = (0, 4, 0),…

A: Equation for plane P is written in vector form as: n.(x,y,z)=d In scalar form equation is written as…

Q: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).…

A: Solution

Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: Write the equation of the plane that is parallel to the xy-plane and passing through the point…

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Q: Find an equation for the plane that contains the line x = − 1 + 3t, y = 5 + 3t, z = 2 + t and is…

A: We need to determine the equation of the plane that contains the line: x=-1+3t, y=5+3t, z=2+t and is…

Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, –1, 2), C =…

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Q: Find an equation of the plane containing the following two lines. х-5 у-4 _2-5 -1 3 -2 х-1 y-3 z-2…

A: The general equation of a plane is ax+by+cz=d where a,b,c are direction ratios(DR) of the plane.

Q: (50p.) l- Find an equation of the plane through (1,3,–2) and the line of intersection of the two…

A: Given that, P1 : x-y+z=1 P2 : x+y-z=1 and Point A(1,3,-2)   We have to find Equation of Plane…

Q: Find an equation for the plane through A(0,0,1),B(2,0,0),C(0,3,0).

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Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: Write the equation for the plane through the points P(-1, -7, 45), Q(2, 3, -6) and R(1, -4, 33).…

A: Here we have to find the equation of the plane through the points P(-1,-7,45),Q(2,3,-6) and…

Q: Determine the equation of the plane that contains the points P(1,−2,0), Q(3,1,4) and R(0,1, -2)

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Q: Find the equation of the plane passing through three points A (-1, 2, 1), B (1,0, -2) , C(1, –1,1)

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Q: Find an equation of the plane containing all of the points below: P: (3, -2, -1), Q: (1, 1, 1), R:…

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Q: Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

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Q: Find an equation for the plane through A (0,0,1),B(2,0,0),C(0,3,0).

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Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and O(2,-3,4).

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Q: Find the equation of the plane that contains the following two lines: I = -1+t, L1 : y = -t, I = -1,…

A: To find the equation of plane containing both the lines

Q: Find the equation for the plane through the points Po(4,2,5), Qo(- 3,1, - 1), and Ro(-1,- 2,3).

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Q: Find an equation for the plane that passes through the following points. (2, –1, 4), (0, 0, 6), and…

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

Q: Find the equation of the plane which contains the line ( 2 + t , 3 − t , 4 + 2 t )and the point ( 0…

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Q: Find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R = (2,…

A: To find an equation for the plane containing the three points P = (1, 2, 3), Q = (3, 1, 2), and R =…

Q: Find the equation of the plane through the point P = (3, 2, 5) and parallel to the plane a + 3y+ 3z…

A: Given: Line is parallel to x+3y+3z = 5 Equation of the plane parallel to the plane x+3y+3z = 5 is…

Q: Find the equation of the plane for all points equidistant to (1, -1, 1) and (0, -5, -2).

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Q: Find an equation of the plane each of whose points is equidistant to the point H(4, 2, 5) and to the…

A: Basic 3D Geometry problem

Q: Find an equation for the plane that passes through the point (-1, 6, 0) perpendicular to the line x…

A: Direction ratios of line x =-1 + t, y = 6 - 2t, z = 3t are  <1,-2,3> .Sine line is…

Q: Find an equation of the plane through the three points given: P= (0,0, 1) , Q =(-1,4,2), R=(-2,–2,…

A: We have to find the equation of a plane which passes through the following points -  P = (0,0,1) Q =…

Q: Find an equation for the plane passing thnrough the given points: Р(- 4, — 1, — 1), Q(- 2, 0, 1). R(…

A: Given that: Points P(-4,-1,-1), Q(-2,0,1), R(-1,-2,-3)

Q: Write the equation for the plane through the point P(- 4,4,2) and perpendicular to the line x =4+7t,…

A: Explanation of the answer is as follows

Q: Find the equation of the plane through the point (1,4,7) and perpendicular to the line x = 2 + t, y…

A: If the plane is perpendicular to the line, then the line is also perpendicular to the plane.  So the…

Q: Find the equation of the plane passing through the three points A = (-1,0,2), B= (2, –1,2), C = (3,…

A: Given problem:- Find the equation of the plane passing through the three points A = (- 1, 0, 2) B =…

Q: Write the equation for the plane through the points P(-1, 1,-12), Q(2, 8, -49) and R(1, -6, 45). 4x…

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Q: Find an equation for the plane through points P(1, -1,2), Q(2,1,3) and R(-1,2,–1).

A: This question can be solved by applying the formula of equation of plane passing through three non…

Q: 6. Find the equation for the plane through the points P0 (1,−2,−3)​, Q0 (−5,−1,5)​, and R0 (1,0,3).

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Q: Find the point of intersection of the lines L1 and L2 and determine the equation of the plane that…

A: Point of intersection of two lines in 3D

Q: Find an equation of the plane that passes through the points P, Q, and R. P(1, 2, 3), Q(2, 3, 4),…

A: Given, The points are P (1, 2, 3), Q(2, 3, 4), R(3, 6, 9).

Q: Find the equation of the plane passing through the three points A = (-1,0, 2), B = (2, -1, 2), C =…

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Q: Find an equation for the plane through A(-2, 0, -3) and B(1, -2, 1) that lies parallel to the line…

A: Given points are

Q: Find the equation for the plane passing through the points P₁ = (-2,5, -2), P₂ = (-2, 0, 0), and P3…

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