3 Let aj = -1 a2 аз bị 5 5 3 -1 3 b2 -3 b3 2 and n = and let %3D -2 -2 A = {a1, a2, a3} and B = {b1, b2, b3}. Find a hyperplane H %3D %3D with normal n that separates A and B. Is there a hyperplane parallel to H that strictly separates A and B?

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…

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Q: Trapezoid PGRS with vertices P(-6, 2), G(-2 -0, R(-2 -3), and S(-6, -6), reflect in the linex-1 (4)…

A: We need to draw transformed image.

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Q: The vertices of the hyperbola y = 5+ ( x² + 9 )0.5 are Select one: O(0,-3) and (0,3) O(8,0) and (…

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Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

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Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find all point cs) 2= 8- 3x2- 2y2 マh where the fameyent plane orlhugana l i's to とk 2ihe. X 2-31,…

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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: #5

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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: 3. Evaluate ff(+2y- )dS where S is the portion of z = 5= 2y + that lies over the triangle in the…

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Q: Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and…

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Q: Determine the vertices of the hyperbola. (y - 3)2 - (x + 5)2 = 1 4 9 (х, у) %3D (smaller y-value)…

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Q: 3. Rhombus KLMN with vertices K(-3, 2), L(1, 4), M(-1,0), and N(-5, -2): (x, y) → (x, y- 5) 4. Re…

A: First we draw Rhombus KLMN and then Draw Rhombus K'L'M'N' .

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Q: Find the distance between the planes. 5x-2y+z-4 0, 5x-2y+z+6= 0

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Q: Determine the length of the latus rectum of the following conic section: 16z + 9y? - 64.x- 54y+1 0 O…

A: 16x2+9y2-64x-54y+1=016x2-64x+9y2-54y=-116(x2-4x)+9(y2-6y)=-116(x2-4x+4)+9(y2-6y+9)=-1+64+8116(x-2)2+…

Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

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

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

A:

Q: 4. Calculate the distance between the point Q(3, 1, 7) and the plane 2x-6y-z=3. Don't use a formula.…

A: Given point Q(3,1,7)and the plane 2x-6y-z=3. The objective is to find the distance between the point…

Q: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

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Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

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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…

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

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: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

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Q: e find aplane through Po (2,,,-1) and Perpendicular to the line of Intersection of the planes…

A: Equation of plane

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Q: B': 3. Trapezoid FGHI with verlices F(-5,-2), G(-2,-2), H(0, -6), and (-8,-6): y-axis F': H: G: I':

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Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25

A: The equation of the sphere: - The general equation of a sphere is (x – a)2+(y-b)2+(z-c)2=r2 if (a,…

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A: Below are graph and input view.

Q: 1. Find the plane which contains the point M (4, 5,0) and the line 2+3 = ¹ = 2²

A: To find the plane which contains the point M4, 5, 0 and the line x+35=y-4-3=z-22.

Q: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

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Q: Which of these planes pass through the origin? Зх — 5у+ 2z 30 5х — 3 %3D 0 = 4х + у %3D 0 — 4х — 5у…

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Q: The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is D =…

A: topic = planes

Q: 8. If the vertices of a triangle are A(8, 5), B(-1, 8) and C(2, -1) where would the centroid (Center…

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Q: 29. Find the vertices of the hyperbola. (y-8)? 4 (+12)2 6. 3D1 O (-9, 8), (–15, 8) O (-10, 8), (–14,…

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Q: 3. 4. Circumscribing the triangle with vertices (a, U), (a, d), (U, %). 2a = 0. Ans. z2 + y+ ax- ay…

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Q: 4) Find equations for the planes: a. The plane through P(0,2,-1) normal to n = 3i-2j-k

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Q: 6. Find a parametric representation of the line of intersection of the two given planes. 2x+ y- z= 6…

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Q: -20 -15 -10 -5 5. 10 15 20 For the graph of hyperboloid of two sheets () - A`- A'-: 1, find…

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