Find the intersection of the following geometric objects: the plane 3x - y + z = 3 and the plane 2x + z = 0.

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

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: (d) Find the Cartesian equation of the plane that contains both the line L2 and the point A

A: Introduction: The scalar product of two vectors OA and OB is given by, OA·OB=OAOBcosθ The vector…

Q: Use the plane shown below to answer the questions. Let A = 3, B = 4, and C = 24. (a) Find an…

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Q: draw the plane given by the equation  x + y + z = 0

A: x+y+z=0 It is a plane passing through origin.

Q: To find the equation of a plane which cuts intercepts a, b, c res- pectively on the axes of…

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Q: Write the intersection of plane UVYZ and plane SVWZ? T.

A: given figure is pointed by vertices S, T, U, V, W, X, Y, Z

Q: Find the intersection of the following geometric objects: the plane 3x + 2y - z = -9 and the line…

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Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

Q: Consider the plane with equation 3x – 2y + 4z =7. A point has x coordinate 1 and y coordinate 2. If…

A: We have to find z coordinate

Q: M (1; -2; 4) parallel to the OXZ plane

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Q: Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2,…

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Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Determine the Cartesian equation of the plane that contains the line = (7,2,-1)+ a(4,5,1) and…

A: Given problem:- Determine the Cartesian equation of the plane that contains the line = (7,2,-1) +…

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

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Q: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: Perpendicular to i = 2ỉ - 33 + 5k and through (4, 5, –2).

A: Here is the solution of the given problem. Co-ordinate Geometry 3D - Plane.

Q: Find the equations of planes that just touch the sphere (r- 1)² + (y– 5)² + (z - 4)² = 25 and are…

A: Given : Equation of sphere (x - 1)² + (y - 5)² + (z - 4)² = 25

Q: Find the Cartesian equation of the plane containing the points A(4,0,4), B(1,5.5) and C(-1,-1.2).…

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Q: X-2 4 y+3 -1 z + 2 3 {3х + 2y + z + 2 %3D 0, х -у+ 2z-1 %3D 0}

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Q: Find the Cartesian equation of the plane containing the points A(- 1,0, 1), B(2, 1, 3), C(4, – 2,…

A: topic - equation of plane through three points

Q: Is the line x = 1 + 2t, y =-2 + 3t, z =-5t related in any way to the plane -4x - 6y + 10z = 9? Give…

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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: Determine the equation of the plane that contains the points P_0 = (1, 0, 0), P_1 = (0, 1, 0) and…

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Q: Find an equation of the plane satisfying the given conditions.

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Q: Sketch the plane defined by the equation T1:2x – 5y – 10 = 0.

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Q: Find the standard equation of the plane that contains three points A(1,0,-1) B(2,1,1) and C(1,2,-3).

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Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: 2. Do the two planes intersect? If they do, where do they intersect? TT 2x - y + z = 1 = 0 3 TT 4 x…

A: Equation of the line perpendicular to the given plane be n1 & n2 . Now here n1≠ k n2  , where k…

Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: Is it possible to find a plane perpendicular to both i and j? Explain why.

A: The objective is to find a plane perpendicular to both i and j, if possible.

Q: Find the equation of the plane that contains the line r¡(t) = (1 + lt, –1+t, 2+ 8t) and the point…

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Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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Q: Find the equation of the plane passing through the points A(2,2,1), B(9,3,6) and perpendicular to…

A: Here we have to find the equation of the plane passing through the points A(2,2,1) ,B(9,3,6) and…

Q: Find the equation of the plane that contains the point A(1, 2,-4) and is perpendicular to the…

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Q: Find the angle between the plane -2x +y-2z 0 and the plane generated by the points P1(0, 0, 0),…

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Q: Find the equation of the line of intersection of the following two planes: Plane A: 2r – 3y + 2z =…

A: Given Plane A : 2x - 3y + 2z = 5Plane B : x + 2y - z = 4To find the intersection point, Put z = 0 ,…

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

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Q: Find the equation of a plane through the point (3, -2, 8) and parallel to the plane z = x+ y. Leave…

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Q: Let u = 2 and v = | 0 , and let P = span{u, v}. Find an equation for the plane P.

A: Given: Let xyz be a point in Span {u, v} so there are t, r∈ℝ such that xyz=tu+rv. So,…

Q: Consider the plane shown in the following figure: Let 4, b, c, d 40. A general equation…

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Q: The graph of (x/a) + (y/b) + (z/c) = 1 is a plane for any nonzero numbers a, b, and c. Which planes…

A: Given equation of plan is xa+yb+zc=1   ...(1) Where a, b, c≠0

Q: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

Q: Two automobiles are driving on a plane. The first automobile is moving north at 10 m/s and rising 5…

A: Let's consider North as +ve y-axis, East as +ve x-axis, and upward motion to be +ve z-axis. Now, the…

Q: Determine the Cartesian equation of a plane that is perpendicular to the plane x - 2y + z = 6 and…

A: Given : A plane x-2y+z=6 and which contains a line -x+2-3=y+1=z+12  To find: The Cartesian equation…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.