Give an example of (v1, v2, v3) and (w1, w2, w3) independent se- quences in the R“ such that dim(span(vı, v2, v3) N span(wi, w2, w3)) = 2 and {v1, v2, v3}N {w1, w2, w3} = 0).

Q: Q1 Consider the planes. 7: 2x-y+z = 6, : x+y+22=3,, 3x-4 y+sz=10 : 2x-y +2=3,52-3y+22=1, Find the…

A: Consider the planes: π1: 2x-y+z=6, π2: x+y+2z=3, π3: 3x-4y+5z=10 and  π4: 2x-y+z=3 .   Find angles…

Q: Consider the right triangle withvertices (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

A: Given right angle triangle has vertices  (0, 0), (0, b), and (a, 0), where a > 0 and b > 0.…

Q: Find the line of intersection of the planes z + 2y – z = 1 and z + y + z = 1. Lütfen birini seçin:…

A: Given equation of plane is x+2y−z=1 and x+y+z=1. We have to find the line intersecting of the plane…

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: Find an appropriate parametrization for the given piecewise-smooth curve in R'. The triangle formed…

A: Given that the triangle formed by travelling from the point (1,2,3) to (0,-2,7), to (6,4,2) and back…

Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

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Q: Find a vected that is Perpenditular to the Plane that Contaiins the e poin +s P(2,3,4), Q~2)0,5), R…

A: Given: The three points:  P (1 , 3 , 4 ) , Q ( - 1 , 0 , 5 ) and R ( 4 , 2 , 2 ).   To determine: A…

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

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Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: 2. Show that the xy plane W = (x, y,0) in Rº is generated by: (i)u = and v = (ii)u : and v = 3

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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: where P is the parallelogram Spanned by the Vectons 24,13 and <3,3) with tHanformation X=4u+3V and.

A: Given that ∫∫Pe4x-ydxdy where p is the parallelogram spanned by the vectors 4,1 and 3,3 with…

Q: 4. In a rhombus WXYZ, WXY = 108°. Find () XY, (ii) XỸZ, (iii) XÂWY. %3D

A: Answer: Given W X^ Y =108° →(1) In a rhombus the diagonals bisect the angle at the vertices→(2) The…

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Find the line of intersection of the planes 2x – y+ 3z = 1 and -r + 3y + z = 4. Lütfen birini seçin:…

A: Given planes are 2x−y+3z=1 and −x+3y+z=4. We have to find the line of intersecting of the plane…

Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Let (x,y,z) be the point which is closest to the point (2,4,0) .

Q: Q) show that the pánts ACI,1,4), B(2,2,2), C (o,1,5) and D(1,0,5) ave coplanear (in the Same plane).

A: The given points are: A=1,1,4B=2,2,2C=0,1,5D=1,0,5 To prove: A, B, C and D are coplanar (they lie in…

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 fvelume of Solid f in the octant that is below porabalord そこ16-メ-9 planes X:0,9:0I and Z=0. and…

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Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

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: Use Green's theorem to calculate where C is the rectangle with vertices (0, 0), (2, 0), (2, 3), (0,…

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Q: evaluate $ A. dš over the sphere R = 3 and show whether Divergence theorem holds or not. %3D

A: Calculate surface integral over R=3 or dr=0 ∮A→×ds→=∮R cos2θ,π,0×r2sinθdθdϕ,rdϕdr,rsinθdrdθ…

Q: The sphere x² + y² +z² = 100 has the center (0,0,0) and a radius of length 50. Select one: True…

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Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: Verify Divergence Theorem for by co-ordinate planes and the plane 2 x + y + 2 z = 6. F = (x+ y³) i –…

A: Given that F=(x+y2)i-2xj+2yzk The divergence theorem is, ∭FdV=∭∇Fdxdydz On surface S1, y+2z=6,…

Q: 2. Show that the xy plane W = (x, y, 0) in R³ is generated by: (i)u = 2 and v= |1| (ii)u and v = 3…

A: Given the plane: W=(x,y,0) in ℝ3.Let (x,y,0) be any element from W. For a and b in ℝ, we…

Q: Find all planes which (i) are tangent to the elliptic paraboloid z = x² + y², and (ii) pass through…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the distance between the planes 4x + 5y + z = 25 and 4x + 5Y + z = 53. %3D

A: Explanation of the solution is given below....

Q: Find the maximum value of f(r, y) = 10ry(4 – 8z - 4y) over the triangle with vertices (0, 0), (,0)…

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Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: Find m, n ∈  R so that the line r X: (n, 2,0) + λ (2, m, m) is contained in a plane π: x -3y + z = 1

A: The direction cosines of the line, r(x)= (n, 2,0) + λ (2, m, m) are &lt;2, m, m&gt; . The direction…

Q: Show that there are point(s) (x, y, z) satisfying 2x − 3y + z − 5 = 0and lying on the line v = (5,…

A: The given equation of the line is

Q: An _____ is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and…

A: The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a…

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: Let S be the portion of the cylinder y = 1 - x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

A: Consider the given information. The formula for the double integral is defined as.…

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 and 2r + y -…

A: The equations of the two planes are: 3x-6y-2z=152x+y-2z=5 As, 5,0,0 satisfies the equation of plane…

Q: Evaluate //R V2x(y – 2x)dA where R parallelogram on the xy-plane with vertices (0, 0), (0, 1), (2,…

A:

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: Evaluate the double integral / ydrdy where T is the triangle with vertices (0,-1), (0, 5), (4, 3).

A: First, draw the region of integration. Then, use the region to setup the double integral.

Q: Show that a indeed perojective plane of gives 0rder BİBD (n+n+,n+),!

A: We need to prove that a projective plane of order n indeed gives a BIBD (n2+n+1, n+1, 1)

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

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Q: Use Green's Theorem to find work done by F = 2°yi + (y – 3)3 along the curve c, C is the closed path…

A: We will find out the required solution.

Q: Let S be the portion of the cylinder y = 1 − x2 with x≥0; y≥0, bounded by the planes z = 2, and z =…

A: