Let T be a tetrahedron in "standard" position, with three edges along the three positive coordinate axes in R3, and suppose the vertices are ae¡, be2, ce3, and 0, where [e e, e; ] = I3. ez ] = 13. Find formulas for the barycentric coordinates of an arbitrary point p in R3.

Q: Which of the following solids can be formed by the above net? A В D

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

A: Sketch the tetrahedron T with vertices (2,0,0), (0,3,0), (0,0,5) and the origin.

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: Consider the parallelepiped with adjacent edges u = 8i + 5j +k v = i+j+5k w = i+ 8j + 8k Find the…

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Q: Let C denote the triangle with vertices at (0,0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: Use Green's theorem to find this integration.

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A: From a point S(x0,y0,z0) to the plane M = ax+by+cz+d=0 Let S1=x1,y1z1 be any point in the given…

Q: Let ABCD be a trapezoid with bases BC and AD. Let 0 = AB n DC be the point at which the lines…

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

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Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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Q: Let S be the solid tetrahedron bounded by the four planes a = 0, y = , z = 30, and z = 4x + y. !!…

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Q: Let M C R³ be the set obtained by rotating the circle {(x, 0, z) E R³ : (x – 2)² +2² = 1} about the…

A: Solution is given below

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: Given points are CX,,8,).(X,%%),CXo,Y) in the plane, with X, <Xz <Xg. Use det V = (X2-xi) (Xg- X.)…

A: Given the points x1,y1, x2,y2, x3,y3 in the plane with x1&lt;x2&lt;x3. We need to figure out the…

Q: 14. Find the volume of the parallelepiped having i + 3j + 2k, 2i + j- k and i- 2j + k be the edges.…

A: The edges of the parallelopiped is given to be a=i+3j+2k, b=2i+j-k, c=i-2j+k. To find the volume.…

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 5, 0), (0, 0, 4) and the origin. Write /| f(x,…

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Q: 6. Use Stoke's Theorem to evaluate fF dr, where F =, and C is the part of the paraboloid z = 4 - x2-…

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Q: Show that the maximum value of a^2b^2c^2 on a sphere of radius r centered at the origin of a…

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Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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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: 4) Name a point that is coplanar with A, B, and C. b. E D a. D d. N C. F 3)

A: the given figure we have to name a point that is coplanar with A, B and C.

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: . Consider a two-link planar robot ori- ented in the elbow-down position as shown in Fig. P3.26. If…

A: In this two-link planar robot oriented in the elbow down position, x=-1,y=15,l1=10,l2=8 The formula…

Q: Let E be the solid parallekepiped with vertices Co,0,o).(LLO).co,l,3),(1,0,). C1,2,3),Cし,4).(2,1,1)…

A: Here, vertices are given in 3D. So, for taking limits of X and Y, we'll look for the projection of…

Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Substitute the parametric coordinates of the line in the equation of sphere and solve to get the…

Q: Let C denote the triangle with vertices at (0, 0), (0, 1) and (2, 1), oriented positively. Then f(x²…

A: We have to apply the green's theorem here.

Q: Let C be the cubic region delimited by the coordinate planes and by the planes x = 2 y=2 and z=2 in…

A: the planes x = 2 y=2 and z=2 in the first octant.

Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

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Q: Find the projections of the following onto the base planes of the given figures: i CF B ii DG A D C…

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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: Let R be the triangle in the xy-plane with vertices (0,0),(0, 1),(1,0). Find C[n(2 – x – y) dA.

A: Given vertices of triangle now we have to find the area as shown below

Q: Let z be a complex mumber and fe be any fusction. If C isa closed contour and 4 r)dz =0 dhen %3D

A: By Cauchy integral formula, let f(z) be any function and C be a closed contour satisfying the given…

Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: =7. Consider a two-link planar robot, with positive orientations of 0, and 0, as shown in Fig.…

A: Solution :-

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: Let T be the tetrahedron with vertices (4, 0, 0), (0, 3, 0), (0, 0, 5) and the ori I f(x, y, z) dV…

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Q: Pr. #1) || zdA, Dis the triangular region with vertices (0,0), (4, 2), and (0,6) (aketch D on the…

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Q: ABCDEF is a regular hexagon with centre O. OA = a,OB = b and M is the midpoint of BC. X is the point…

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Q: Consider the parallelepiped with adjacent edges u = 6i + 5j +k v =i+j+5k w =i+6j + 6k Find the area…

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Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 2,0), (0, 0, 5) and the origin. Writel II|…

A: Follow the steps to find the upper limit of x and z to solve the problem.

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: Find c, and cz for the inner product of R2 given by (u, v) = C;u;V2 + Czuzv2 such that the graph…

A: Given the inner product u,v=c1u1v1+c2u2v2 whose length is u=1.   From the given figure, we can write…

Q: Consider the solid Q, in the first octant, which is generated by the surfaces: S1 : x2 = −(z − 3),…

A: Given:  S1 : x2 = −(z − 3), S2 : y + z = 3, S3 : z = 2, S4 : z = 0, S5 : y = 0 and S6 : x = 0  The…

Q: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

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Q: of the Solids ebtaind by-revolding 5 Find the velume of the Sotids abtaind by revolu.ing Yegion in…

A: In this question we have to calculate the volume obtained by the revolution of given two region…

Q: Construct a clamped cubic spline passing through the points d, e and fwith f(x)=x³ + 1 a= 0 . .b=…

A: Consider the given equation: fx =x3 +1

Q: Describe your plan for proving the following.

A: Given that AM=MP and ∠AMP=90o. X can be thought of as a plane ground and AM is perpendicular (pole…

Q: Let T be the tetrahedron with vertices (3, 0, 0), (0, 4, 0), (0, 0, 5) and the origin. Write f(x, y,…

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Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…