f we need to find the equation of a plane when given a point in 3-dimensions and two planes that intersect in a line that is contained in the objective plane, how do we find the line of intersection of the two given planes and then proceed to find two points on that line so that we may find the equation of the objective plane with three points and the cross product (to find the normal plane)? Please do an example with point (3, 1, 4) and planes x + 2y + 3z = 1 and 2x - y + z = -3, and please explain all of the steps and use typefont. Thank you!

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

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Q: 1. Find an equation of the plane that passes through the points (-1, 3, -3), (4, 1, 2), and (8, 2,…

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Q: Represent two planes that intersect at a line represented by 3. y- 7 = z+2 2.

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Q: Find an equation of the plane that passes through the point (3, 1, 4) and contains the line of…

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Q: Does the point (3, 2, -2) lie on the line through C(-1, 4, 5) and D(3, 2, 8)?. In each system, at…

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Q: Find an equation of the plane perpendicular to the line through (2, 2, –4) and (7, –1,3) and…

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Q: A plane is passing through the points A(0,1,3), B(-1,2,0) and C(3,-2,4). Find

A: The vector form of the equation of a plane is given by the expression (r→-a→)·(b→-a→)×(c→-a→)=0.…

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 an equation of the plane passing through the three points given.P = (2, −1, 4), Q = (1, 1, 1),…

A: To find the equation of the plane passing through the three pointsP =x1,y1,z1= (2, −1, 4), Q…

Q: Find an equation of the plane passing through the given points. (a) (0, 1, 2), (3, −2, 5), (2, 3, 4)…

A: I will Solve (a) for you,   Given Points are, A=(0,1,2) B=(3,-2,5) C=(2,3,4) We have to find the…

Q: Find an equation of the plane passing through the three points given.P = (5, 1, 1), Q = (1, 1, 2), R…

A: GivenP=(5,1,1) , Q=(1,1,2) and R=(2,1,1)To find equation of plane passing through the three points.

Q: Find an equation of the plane that contains the points (1, 2, 3), (3, 3, 2), (2,3, 5).

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Q: Find an equation of the plane that contains all the points that are equidistant from the given…

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Q: Find an equation of the plane passing through the points.(−4, −4, −4), (4, −1, −4), (−4, −1, −4)

A: Here given as

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

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Q: 4) Find the equation of the line of the intersection of the planes -2x+3y+7z+2=0, x+2y-3z+5=0.

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Q: Is Span({(4,–10, 6), (-6, 15,–9)}) a line or a plane in R³? Why?

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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 symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

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

A: Equation of plane

Q: 9. Determine the number of points of intersection for the planes: ₁:3x-6y + 12z - 6= 0 and ₂: 2x -…

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Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: Find the equation of the plane through (-1,6,2) and perpendicular to the join of (1,2,3) and…

A: We have to Find the equation of the plane through (-1,6,2) and perpendicular to the joining of…

Q: Find the plane that contains:  P1(-1,1,-2), P2(-2,2,4),P3(0,2,-2)

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Q: 4- Find an equation of the plane that passes through the given points (-2, 1, 1), (0, 2, 3), and (1,…

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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 by…

A: we know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: 2. Find the equation of the plane through the points (1, -3,2), (3,0,– 1), and (0,5,5).

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Q: Find the equation of the plane that passes through the points P1 = (2, 3, 1), P2 = (5, 4, 3), P3 =…

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Q: In a geometry class, students are asked to describe the dimensions of a plane based on the…

A: In a geometry class, students are asked to describe the dimensions of a plane based on the…

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: The planes 3x - 2y + 4z - 7 = 0 and -2x + 3y - z + 6 = 0 are perpendicular. Select one: True False

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Q: Find the eu. f line through the Pont (-2,3,4) and Parallel to e Planes: 2x +3y +42-5, 3X+4y+52 - 6…

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Q: The equation of the plane that contains the three points (0, 4, 4), (4, 0, 4), and (4, 4, 1) is

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Q: as If the equation of plane passing through the mirror image of a point (2, 3, 1) with respect to…

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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 equation of the plane through (-1, 6, 2) and perpendi cular to the jain of (1, 2, 3) and…

A: Given,           The equation of the pane through -1,6,1 and perpendicular to the join            of…

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: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

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Q: 4) Find the equation of the line of the intersection of the planes -2xr+3y+7z+2=0, x+2y-3z+5=0.

A: We have two equations in three variables. To find the line of intersection of these planes, we fix…

Q: Determine the equation of the plane that contains the points (3, 4, 1), (1, 7, 1) and (-1, -2, 5)

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Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: 3. What are the three possibilities for the intersection of a line and a plane?

A: The solution is given in the next step.

Q: The line passes through the point(7, 8, 9) and is parallel to the xz-plane and the yz-plane. 7,8,1 +…

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Q: Find the equation of the plane that passes through (3,4,-1) and contains the line of intersection of…

A: To work out the equation of the required plane satisfying the given geometric conditions

Q: Find an equation for the plane passing through the points (– 5, 2, 3), ( – 1, 2, 5), and (– 2, – 3,…

A: We have to find equation of plane Passing through 3 points.

Q: Find the points at which the line that passes through (–6,6,4) and (12,–6,2) intersects the three…

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

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Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

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

A: Let's find.

Q: In a geometry class, students are asked to describe the dimensions of a plane based on the…

A: The statements given by students are Mark states that a plane has zero dimensions because it is made…

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.