Find the point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200 -14/ 625 V 1200 13v 625 1200

Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: Which of the points A(9, 0, 3), B(6, 5, 6), and C(2, 9, 2) is closest to the yz-plane? Which point…

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Q: nd the distance from the point to the plane.   (3,3,8)​, 7y+3

A: Given, the equation of plane is                                       7y+3z=0and  point (3, 3, 8)

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

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 point on the sphere x2+y2+z2=1089 that is farthest from the point (-22,-17,-21).

A: Let, (x,y,z) be the point on the sphere g(x,y,z)=x2+y2+z2-1089=0...(1) which the maximum distance…

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

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Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

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Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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Q: Find the standard equation of the sphere. (Let  r = 9 and C = (3, 8, 9).)

A: equation of sphere where center ( a, b ,c ) radius r

Q: I just need #20

A: Given,

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: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Show that the distance between the parallel planes                                          ax + by…

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Q: close

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Q: 5.4. F(х, у, 2) 2³), M is the outer surface of the sphere x² + y² + z² = a². %3D

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Q: Find the distance from (−2, 4, 5) to the plane 2x + 6y − 3z = 10.

A: we know that distanced of pointx1,y1,z1 from the plane ax+by+cz=d is given by…

Q: Which point(s) lie in the plane 2x + y - z = 10? a) (0, 0, 10) c) (2, 4, - 2) b) (5, 3, - 3) d) (-3,…

A: Given:plane: 2x+y-z=10

Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: Let P(-5, -3, -7) and Q(7, 11, 1) be two points in three dimensional space. Write an equation of the…

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Q: Find the value of x and y in the rhombus. yo 3x° 2x° y = IL ||

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Q: Identify and sketch the quadric -- = 0 3 2 3 surface z 2

A: For the solution of the problem follow the next step.

Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

A: Given, x2+y2+z2=1   ;   point (2,1,2)

Q: Find the point on the sphere x2+y2+z²=529 that is farthest from the point (-7,-11,-29).

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Q: Show that the equation represents a sphere, and find its center and radius: x^2+y^2+ z^2-8x + 6y +…

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Q: Find the standard equation of the sphere. (Let r = 5 and C = (9, 7, 5).)

A: Standard equation of a sphere with radius r and centre at c=(h,k,l) is  (x-h)2+(y-k)2+(z-l)2=r2

Q: Calculate the shortest distance between the point P = (3, 2, 2) and the plane 5x+y-2z = 3. (Do not…

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Q: Find the shortest and longest distance from the point (1,2, -1) to the sphere x2 + y? + z? = 24 %3D

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Q: find the distance from the point to the plane. (6, 0, -6), x - y = 4

A: x1,y1z1=6,0,-6…

Q: Find an equation of the largest sphere contained in the cube determined by the planes x = 0, x = 8,…

A: given the planes:

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

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: r = (6,-3,2)+1(2,0,1) + u(1,1,–3)

A: Given point is (0,-1,-8) and the plane is r→=6,-3,2+t2,0,1+u1,1-3

Q: Try to visualize the set of all points (x, y, z)in a coordinate space that are twice as far from the…

A: a) Suppose the distance between two points  A(x, y, z)  and the origin   Plug into the distance…

Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O…

A: topic - shortest distance between point and sphere

Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: 4 2 + Find the area of the portion of the Sphere x² + y² +2²= 9 between the planes Z=1 and 2 = 0.…

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Q: Find the point on the plane 3x+4y+z=8that is nearest to​ (2,0,1). What are the values of​ x, y,…

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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: Find the center and radius of the sphere x2 – 12x – 4 +y? + 4y + z? – 20z = 0 ОА С (6, - 2,10), r…

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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: Which of the points A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) is closest to the yz-plane? Which…

A: Given- A(−4, 0, −1), B(3, 1, −5), and C(2, 4, 6) To do- 1.Which of the points A(−4, 0, −1), B(3, 1,…

Q: Find the distance from the point (7,-9,-5) to the plane 3x + 5y = 51.

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Q: Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point…

A: Given sphere, x2+y2+z2=1 Consider gx,y,z=x2+y2+z2-1=0 The square of the distance between the points…