(c) A Plane LMQ B Plane LN C Plane Q DQ E Plane LMN Plane MNL

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

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Q: Determine the Miller indices of a plane that makes intercepts of (4, 3 and 8) on the coordinate axes…

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Q: A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1.…

A: A set W is defined as consisting of all the planes in R3 that are parallel to the plane x+2y-3z=1.…

Q: Answer the fallowing muitiple-chorce awestion below algubra #11,K is aveal nmber and e is the lime…

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

A: Given that: The vertices of a rhombus are: W(1,5), X(6,3),Y(1,1), Z(-4,3)

Q: Determine the basis for a plane that passes through the origin at R³ and for a line that passes…

A: A general equation for a plane passing through origin is ax+by+cz=0. Now, z=-acx-bcy. So,…

Q: Vaughn Pang sketched trapezoid RUIZ on a coordinate plane. RUIZ has vertices located at R(1,4),…

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Q: Above the paraboloid z= 6-x-y² and under the plane z= 9 for x? +y? < 4 .

A: volume by double integral using  polar coordinate

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: 9. What is the xy trace of the sphere (x – 5)2 + (y – 2)² + (z – 10)² = 16 ? а. (х — 5)2 + (у — 2)2…

A: To find the xy trace of sphere, put z=0 in equation of sphere.

Q: Sketch the following planes in the window [0, 5] × [0, 5] × [0, 5]. The plane parallel to the…

A: First obtain the plane that parallel to the xz-plane containing the point (1, 2, 3).…

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: Find the volumes of the regions

A: The Volume of  the wedge, where D is the solid and R is the region, is calculated as,…

Q: Consider the design given by the general finite projective plane P2 (F,), where p is a prime number.…

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Q: Use Green's theorem to find $ x? ydr + xdy over a counterclockwise triangular path passing though…

A: To find the line integral ∮x2ydx+xdy by using Green's theorem, First, we need to draw the given…

Q: Find the distance from the point (-2, 1, 4) to the a. plane x = 3 b. plane y =-5 c. plane z =-1

A: Given:The point (-2, 1, 4).Formula:The distance between a point (x1, y1, z1) and the plane  is,

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Evaluate // x² zdS, where S is the part of the S 1 + 4x + 3y above the rectangle plane z = [о, 2] x…

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Q: (1.5) 1.) brejech on flive the bisecter ar-1= 2-y=32+ in the plane In me plane

A: 1.6 . Projection of a line onto the plane is either a point or a line. Projection of A onto the…

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

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Q: ind the equ.of Plane that Contains plos1,3) and Parallel to the X-2 Plane and PerPendicular to the…

A: Solution:-

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

Q: Find all planes in R3 whose intersection with the xy-plane is the liner( t) = t ( 2, 1, 0) .

A: GIVEN  Intersection with the xy-plane is the line r( t) = t ( 2, 1, 0)

Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: 13) find the equ.f Plane Parallel From (3,2,-1) is twise ther distunce to the Plane 2X-9 +22=1 to…

A: Solution is given below:

Q: 12) Find the intersection of the plane: x – z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: is ndicular tò the plane containing the points: A = (-1,1, 2) B = (-3, 2, 1) C = (5 – 1, 1) the

A: Given that the plane is passes through the point A, B and C. We have to find the normal vector of…

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: Aa, Bb, and Cc are medians of triangle ABC with centroid at G , if aG = x, what is AG?  a. x b. 2x…

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Q: 4. Find an equation for the plane in R spanned by the points (1, 5, 1) and (1,4, 2).

A: Given v1 = (1 , 5 , 1)v2 = (1 , 4 , 2) Let xyz be a point in spanv1 , v2 , so there exist m , n…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: O Find an equahion for the plane throught (1,-,3) parallel to the plane 3xy+Z=7

A: According to q&amp;a guidelines I can do only 1question

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: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: find the line of intersection of th e given planes. 3x + 2y + z = -1 and 2x - y + 4z = 5

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Surface o is a plane a +y + z = 1 that lies in the first octant. Evaluate

A: Given, surface σ is a plane x+y+z=1 that lies in the first octant. To find              ∬σ(2x+z)dS=…

Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

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: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain

Q: Let S be the triangular prism with the triangular face in the plane y-3 removed. Let C be the…

A: Given curl F→=xi^-yj^ and the given plane is y=3 So, ϕx,y,z=3j^ Therefore, calculate curl F→·n^ curl…

Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

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Q: be Sreal number. Explain why the planes a X + 2y + az = 1 and ax + 2y + az = 17 are not osethogonal

A: Let θ be the angle between the planes.A1x+B1y+C1z=D1 and A2x+B2y+C2z=D2then cos…

Q: Find the coordinates of the point Y that lies 2. along the directed line segment from X(-1,3) to…

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Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Consider the following. z = 1 Sketch a graph of the plane. 10 tz 10 5 10 10 10 10 10 tz 10 tz 5 0.…

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Q: 3 FIND TiHE GENERAL FORM (SIMPLIFIED AS WELC) OF THE PLANE (1,0,5), (2,10, 6) (-),2,3) CONTAINING

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Q: The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz-…

A: According to the given information it is required to set the double integral to find the volume of…

Q: Let P be the plane 2r + u – 7 = 2 and let 0(1.0.3) be a poir

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