The center of the sphere whose one of its diameters has end points P1(1,-3,-1) and P2(2,0, 1) is A)(3, -3,2) B)(1.5, 1.5 , 1) C)(0.5, 1.5, 1) D)(1.5, – 1.5,0) -- E)(-0.5,-1.5,-1)

Q: Find the coordinates of the centroid of the triangle with the given vertices. X(1, 4), Y(7, 2), Z(2,…

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Q: What is the center and radius of the sphere whose equation is (x + 1)2 + y2 + (z + 4)2 = 5? (-1, 0,…

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Find the equations of planes that just touch the sphere (x – 4)² + (y – 5)² + (z – 2)² = 16 and are…

A: Sphere equation x-42+y-52+z-22=16

Q: b) Show that the points A = (1, 2, 2), B = (3,4, 5) and C = (-1,0, –1) lie on a plane through the…

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Q: Find the centroid (ã, §) of the triangle with vertices at (0, 0), (2, 0), and (0, 8). || 18

A: Recall: Centroid of a Triangle with vertices are (x1,y1) , (x2,y2) and (x3,y3) is…

Q: A sphere in the first octant is tangent to the three coordinate planes. What is the radius of the…

A: Given:- A sphere in the first octant is tangent to the three coordinate planes To find:- Radius of…

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: prove that the three planes 2x+y+z = 3 , x-y+2z = 4, x+z = 2 from a triangular prism and find the…

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Q: Find the distance (in appropriate units) between the points P(2,−1)P(2,−1)and Q(3,4)Q(3,4)in the…

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Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: Determine the coordinates of the center and the value of the ra sphere x2- y2-2- 10x - 6y - 12z --54…

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Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: 4. Rhombus WXYZ with vertices W(1, 5), X(6, 3), Y(1, 1), and Z(-4, 3): x-axis

A: Given vertices are: W (1,5)X (6,3)Y (1,1)Z (-4, 3)

Q: Find the point on the sphere  x2+y2+z2=900 that is farthest from the point (−19,−8,11).

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Q: If the coordinates of the mid-points of the sides of a triangle are (1,1) ,(2,-3) and (3,4) .Find…

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Q: show that the points AC!,l,4) B(2,2,2), coplanear (in the c(o,l,5) and D (1,0,5) are Same plane).

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Q: 1. Find the area of the triangle in the R2 plane whose vertices are given by (0,0), (–1,4) and (7,…

A: 1. The Area of triangle with vertices (x1,y1),(x2,y2),(X3,y3) is given by formula : ∆…

Q: The distance between the point (9, 8, 3) and the plane x + y−2z = 5 is _____.

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Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

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Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

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Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

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Q: Find the distance from the point (2, 1,−2) to the plane 6(x − 1) + 2(y − 3) + 3(z + 4) = 0

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Q: A computer software exists so that the cursor of the program and ends at the origin of the plane. A…

A: To determine the distance traveled by the cursor.

Q: Find an equation of the sphere with center (2,-3,6) that touches the xy-plane.

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Q: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Find the center and radii of the sphere 3x2 + 3y2 + 3z2 + 2y – 2z – 6 =3

A: As a first step, let's recall the standard equation for a sphere:The standard form of the equation…

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: The center of the sphere whose one of its diameters has end points P;(1,3, –1) and P2(2,-2,1) is |…

A: Given that the endpoints of the diameter of the sphere are P11, 3, -1, P22, -2, 1 To find its…

Q: what is the intersection of plane  x+2y+z=0 and the line (x,y,z)=(0,1,2)+k(–1,1,2), KER(real…

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Q: A quadrilateral has the following vertices given:  P1 (1, 4), P2 (3, 4), P3 (3, 6), P4 (1, 6).  The…

A: Given points are :  P1(1,4) , P2(3,4) , P3(3,6) , P4(1,6). We will first plot those points in a…

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

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Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

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Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

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Q: Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(−1, −2, −3) &…

A: Introduction: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: Determine the distance from point P(-2, –1, 1) to the plane [x, y, z] = [4, –1, 6] + t[1, 6, 3] +…

A: Parametric equation of a plane is: x,y, z=p+at+bs where a and b are the vectors parallel to the…

Q: Find the distance from the point to the plane. (6, 0, —6), т — у %3D 4

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Q: Find the point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

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Q: Consider the sphere (x−3)2+(y−2)2+(z+1)2=32(x−3)2+(y−2)2+(z+1)2=32. The point P =(−1,2,3)(−1,2,3) is…

A: Given that, x-32+y-22+z+12=32 And the point on the sphere is p-1,2,3 To find another point on the…

Q: ■ Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3)…

A: Distance of a point from plane

Q: Find a plane through the point Po(2, 1, -1) and perpendicular to the line of intersection of the…

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Q: The center of the sphere whose one of its diameters has end points P;(1,3,–1) and P2(2,–2,1) is…

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Q: find the equation of a sphere passing through the point(1,-3,4),(1,-5,2),(1,-3,0) and having on the…

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Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

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Q: What are the projections of the point (3,−2,−7)(3,−2,−7) on the coordinate planes? on the xy plane?…

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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.