4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟ and uz. d = 2.

Q: 4. Consider the point M 2t,31 – 1,-t+ Determine t for that M belongs to the mediator plane of [AD].

A: Question: (4) Given points A-1,4,2,B1,1,0,C-3,5,-32 and D232,15,10 Objective is to find the value of…

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

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Q: [] -3 -3 Let y = -9 uj -5 u2 5 Find the distance from y to the plane in R3 spanned by ul and u2.

A: Consider the provided question,

Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

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Q: 13 - x² – y? at (3, 2, 0), then If the point (1, 1, k) lies on the tangent plane to the paraboloid z…

A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

Q: 4. For the linear canonical system x' = Jx, x € R², determine the nature of the origin as a fixed…

A: Given canonical system x'= Jx  Case-1:-  det >0 if both Eigen value positive:- The product of the…

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: 4 -2 -2 Let y = = 'n: -6 In -9 -2 Compute the distance d from y to the plane in R' spanned by uj and…

A: given  y=29-9 , u1=4-2-2 , u2=-22-6 compute the distance dfrom y to the plane in ℝ3spanned by u1 ,…

Q: (a) Let F = 4x27 + y} - (z – 1)k. Compute I7. dA where S is a square of side 5 units centered at…

A: Given that, the vector is F→=4x2i→+yj→-z-1k→. Determine the value of ∫SF→·dA→.…

Q: 3. Compute the inner product g (v,w) of v = + x. 2 əx and w = x.-+ 2y. Əx ay' Where the line element…

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Q: 36 Find the equation of the tangunt Hne plane at l'2,1) and f L1.95, to fxiy) = Jao-xa - Tya %3D use…

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Q: 5 3 - 2 Let y = 1 Find the distance from y to the plane in R° spanned by u, and uz. -2

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Q: 8. Let S be the paraboloid z = a(1 – a² – y²), for z >0 and a > 0. Let F(x, y, 2) = (x – y)î+ (y +…

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Q: Set up the line integral ∫c x2z ds, where c is the line segment from (1, 6, -1) to (- 4, 1, 5). (No…

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Q: Exercise 10.2 Evaluate the line integral fc(² – 2y²) ds, where C is the line segment from (0,0) to…

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Q: (34) Compute SSp (6e3y + 1) dA where D is the solid triangle with vertices (0,0), (1,0), and (1,2).

A: Equation of the linejoining the points 0,0 and1,2  is  y-0x-0=2-01-0  Or,  yx=21=2  Or, y=2x…

Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: 3y i+ 3x j) ·…

A: Given If C is the line segment from (1, 3) to, (0, 0),

Q: 2. Consider a natural cubic spline model with two knots at ci and c2 given by y = Bo + B1r+ B2(r -…

A: Given, spline model, y=β0+β1x+β2x-c13+β3x-c33+∈                         β2+β3=0  ,  β2c1+β3c2=0…

Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: 3. Consider the ra greater across z =1-r² - y² plane and the s and a paramet

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Q: The transfomation takes points from the xy plane to v= 3x Jx=? that takes points from the uv plar V=…

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Q: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: -In Exercises 1–4 compute dA for the given parameterization for one of the two orientations. 1. ¤ =…

A: We need to find dA.

Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

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Q: 3 4 Let y = -7 and u = -6 -4 1 Compute the distance d from y to the line through u and the origin. d…

A: The projection of a vector on a plane is its orthogonal projection on that plane. In simple words,…

Q: 4. Use Green's Theorem of the Plane to evaluate the following closed path integral. xy2 dx+ 2x2y dy…

A: According to green’s theorem closed path integral over the curve C is calculated by,

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

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Q: 6. Let y = 9 , U1 , U2 1 |3| L10] 1 Compute the orthogonal projection of y onto W = Span{u1, u2}.…

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Q: 4 6 Let y = 7 2 40 Compute the distance d from y to the plane in IR spanned by ui and uz d =

A:

Q: 1) Consider the solid Q in the first octant, generat surfaces: z = (y – 3)² + 1, 2r + 4z = 16, 1= 1,…

A: Volume of solid: Let z=f(x, y) and z=g(x, y) be the functions of x and y of a solid, and let x=a to…

Q: 19. Which plane of the followings passes through the origin? x-4y+5z+1/2 =0 2x+3y+7z=0 4x+2y+6z=1 O…

A: If plane passing through origin  then constant value in the equation of the plane is zero.

Q: Let C be the positively oriented square with vertices (0,0), (3,0), (3,3), (0,3). Use Green's…

A:

Q: Consider the Simple Linear Model: 4 = Bo + Biz, + e, where i = 1,...,n, and e ~ IID(0, o?). Suppose…

A: Simple linear regression model: A simple linear regression model is given as y = b0 + bx, where y is…

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

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Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

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Q: 3.4.6 Use Green's theorem in a plane to evaluate of 10x9²³- [(xy²-y) dx + (x + y²) dy] C as a double…

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Q: 1 5 -6 Let y = -1 , U1 = 7 4 -2 Compute the distance d from y to the plane in R' spanned by uj and…

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Q: 4. let f(x, y) = x² – xy + y² – y. find the direction u and Duf at Po(1,–1) for which Duf is the…

A: Given:- f(x, y) = x2 -xy+y2 -y To find:- Direction u and Du f at point p0 (1, -1) for which Du f is…

Q: Given, (2z - z) dz along the directed line segment from -i to 1. What is a parametric form of z(t)?…

A: Given integral ∫Γ2z-z¯dz where Γ is the line segment from -i to 1. i.e., it is a line segment from…

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: Solve ut = upx in the interval [0, 5] with u(0, t) = 0, and u(5, t) = 1 for t > 0 and u(x, 0) = 0…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to other then…

Q: 4 In AVYX, the centroid is Z. Use the diagram to solve the problems. A. If XR = 24, find XZ and ZR.…

A: In given triangle we have: XO=OV, XP=PY &amp; YR=RV Therefore, OY, XR &amp; PV are median of given…

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.