1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

Q: - 5. Consider th gonal to vector (-

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Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

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: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: Prove i = [- 2,5, 1], = [2,1, – 1] and w = [-6,0, – 12] are orthogonal. %3D %3D %3D

A: SEE ATTACHMENTS

Q: Compute the orthogonal projection of i -5 onto the line L through -4 and the origin. proj, (5) =

A: Here we use for product to find he projection.

Q: Compute the orthogonal projection of onto 7. Use the square root symbol 'V' where needed to give an…

A: Given u→ = -996,  v→ = 1-1-1

Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0,0,0) to (4, 4, 4).

A: Given path is:

Q: 3. Two lines in the plane are perpendicular when the product of their slopes is -1. Apply this to…

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Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: (3,8, 0) is u x v = %3D So the cross product of u = (1, 0, 1) and v =

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Q: show that the scalar t that minimizes ||y– tx||

A: In this question, we need to find the t that minimizes ||y-tx||.

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find the linear approximation to ƒ at P0(1, 2,…

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Q: A normal vector to the graph of z = r²y at the point (2, 1, 4) is Select one: (4, 4, 1) О -4, -4, 1)…

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Q: 9. Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

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Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: Suppose ū = (0, -2, –1) and ū = (-4,0, 5). Then: 1. The projection of u along v is 2. The projection…

A: Need to find projection

Q: 14 Verify the given linear approximation at a = 0. Then deter-

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: Compute I ds over the path C : ř(t) = (t², 2t, t²) from (0, 0,0) to (1, 4, 4).

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Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Compute the orthogonal projection of v = [-6   5   1 ]   Onto the line L through [ -2   6   -7] and…

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Q: Find the general equation f the plane passing through P(-!,3,-2) and having n(-2,1,-1) hormal. O so

A: The objective is to find the general equation of plane.

Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: 4 Compute the orthogonal projection of u= 3 onto the line L through and the origin. projz (5) =

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Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Compute the orthogonal projection of v = 3 onto the line L through -2 and the origin. projr (7) =

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Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: 8. [M] Show that {1, cos t, cos? t,..., cos t} is a linearly inde- pendent set of functions defined…

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Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: 10. Show that 1/x, x are linearly independent on (0, 0).

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Q: 18) (Section 9.7) Find the cross product in space u = 3i – 2 j+4k v=i-3j-k

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Q: Compute the orthogonal projection of u = form, not a decimal approximation. onto v= 3 2 Leave your…

A: To compute the orthogonal projection of u=-4-89 onto v=132.

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: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: -4 -8 Let y = 9 and u = -2 -8 7 Compute the distance d from y to the line through u and the origin.…

A: I have appended the formula used in the solution part of the question

Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V where needed to give an…

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Q: Compute the orthogonal projcction of V 10 onto the line L through -3 and the ariqin. 6 ,4

A: Projection

Q: Construct a linear map L(z) = az + 6 that will send the imaginary y-axis to the line v = - u

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Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: 1. The path of a partide i3 qiven by Sut) =<3 lose, a thint 7 find a) Velouity vector and…

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: 4-) Given a line l with direction vector and a plone jo with normal vecter Ñ show that ln=l or inP=Ø…

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Q: (1, 2, 1) on to the line x = 2+ t, y = 3 – t, z = t. Also Find Find the Projection of b = Projection…

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