b- (4, -1, 3} Out(65)= {-3, 2, 1) Out(66)= (4, -1, 3) In[67]= cntr = (a + b) /2 Out[67]= %3: mean ( delete duplicates total more... In Exercises 18 through 20, find the radius and center of each sphere an 18. x +y +z +2y-2z%3D2 19. x +y +z+4x-4y+2z%3= 0 20.3x +3 y +3z2 +6x-y-3= 0 Product 11.3Dot Exercises Exercises 1 through 3 are based on the vectors a = (1, 1, -2), b = (3, -2, 1. Find the dot product of a and b and the dot product of b and c. 2. Find the angle between a and b and the angle between a and c.

Q: f (x, y) = x² + y² – 2x, D is the closed triangular region with vertices (2, 0), (0, 2), and (0, –2)

A: According to the given information, it is required to find the absolute maximum and minimum values…

Q: Let T be the tetrahedron with vertices (2, 0, 0), (0, 3, 0), (0, 0, 5) and the origin. Write (a, y,…

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Q: (3, 4, 2), (–2, 1,0), (0, 2, 1).

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Draw a figure that shows the image of the triangle with vertices (0, 0), (1, 0), and (1/2, 1) under…

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Q: Q5/ Find the volume of the Tetrahedron that is determined by three edge vectors â = [1, 0.-3), 5=…

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Q: C is the hexagon in the xy-plane with vertices (5, −5), (5, 5), (0, 10), (−5, 5), (−5, −5), and (0,…

A: Given : Vertices : (5,-5) , (5,5), (0,10), (-5,5), (-5,-5) and (0,-10) Integral given :…

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: the distance between the two skew lines L and L2. L: x=3+3t, y=-1-4t, z=4+2t. L2: x=6+5p, y=3-p,…

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Q: Which of the given points are the points on the hyperboloid x2-y?+4z2 = 4 where the normal line is…

A: Solution is in step 2

Q: Find the center C(h,k) and radius (a) :of the circle 9. x² + y² – 4x 4 С (4, 3/2), а 3 5 О %3D C(4,…

A: The General Equation of the circle is:

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: Let B be the ball with center at the origin and radius 1 SSS 4(z² + y² + z²)dV = B

A: Explanation of the answer is as follows

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

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Q: Find the equation of the sphere if one of its diameters has endpoints (3, -4, 5) and (5, 0, 11)…

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Q: having ita Ans. Centers: (2, 1), (1, 4). y = 3, 7x +y = 5, and having ita center or. 16. Touching…

A: Topic-circles

Q: Find the points on the cone z = x +y? that are closest to the point (3,-2,0)

A: Solve the following

Q: Consider AB in the coordinate plane below. 10 4. 2. A -10-9 -8-7 l0 1 -1 -5-4-3 -2-1 2. 4. 10 -2 -3…

A: Given: AB¯

Q: Consider the data: 0 1 2 3 4 f(x) -4 -3 -2 5 12 a) Applying the Composite Trapezoidal Rule with all…

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Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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Q: The figure below shows contours of g(x, y) on the region R, with 9 < x < 15 and 6 < y < 12. 12 -2 10

A: given region 9≤x≤15 and 6≤y≤12 using △x=△y=2 find an overestimate and an underestimate for ∫Rgx,ydA…

Q: Which of the following is a point on the sphere with radius r = 3 centered at the point (-1,0, -1)?…

A: We have given a center and radius of sphare

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

A: Double integration need to be done.

Q: | Let w=z² Find the image of the first quadrant in Z-Plane 2

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Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

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Q: Find the equation of the sphere if one of its diameters has endpoints (3, 1, -5) and (5, 5, 1) which…

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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

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

A:

Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: 12- Evaluate JJI (x2 + y? + z?)dvwhere B is a ball with center the origin and radius 5. B

A: Given problem is :

Q: 7. C is the hexagon in the xy-plane with vertices (5, –5), (5,5), (0, 10), (–5, 5), (-5, –5), and…

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Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

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Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0, 0), E (0, 2,0), and…

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Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

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

Q: of the rectangular prism. A=(3,0,0), B=(3,5,0), C= (0,5,0), 0-(0 ₁1 b. Find AB.√ (3-3)2 + (5-0)² +…

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Q: Let T be the tetrahedron with vertices (5, 0, 0), (0, 2, 0), (0, 0, 5) and the origin. Write II|…

A: Given T is a tetrahedron with vertices (5,0,0) , (0,2,0), (0,0,5) and  (0,0,0)…

Q: If & is the solid tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0) and (0, 0, 4) then: z dV…

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Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0,…

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Q: Calculate (x+ y)dA, where Ris a triangular region with vertices (0,0), (3,0) and (3,3).

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Q: 9. f(z) = e'n/4z %3D

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Q: xplain

A: Given: Hypercube Qn,   n≥2 We have to find the reason behind that why hypercube is hamiltonian.

Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: Find the centroid (, j) of the triangle with vertices at (0, 0), (8, 0), and (0, 9). x=

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Q: 3. Trapezoid JKLM with verlices J(-4, 3), K(-2, 7), L(2, 7), and M(3, 3): y- 1 K'C L'C M 111ו

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Q: Find the equation of the sphere if one of its diameters has endpoints (8, -2, 8) and (11, 4, 17)…

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Q: 2 Let w = z². Find the image of the first quadrant in z-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.