-- Compute the orthogonal projection of v = 1 onto the line L through 4 and the origin. 7 projz (v) =|

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: The vector projection of M = 2ax + 3ay + 2az onto P = 3ax + 2ay + 3az is

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Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Question2 Let L: R R be defined by: L Find all possible 一-0 vectors u such that L U2 33

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Q: If u = (0, 2, 3) and v = (1, 3, -1), find the projection of u onto v. 이름다 a) Obl 이유ㅎ ○ c) (1, 1, -1)…

A: This question can be solved using the concept of vector projection of a vector on other vector.

Q: A) compute x the component of x that is parallel to L and x the component of x that is orthogonal to…

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Q: 8. Suppose v1 is a vector of all entries 1 in R"¹ space, which we call "1-vector". What is ||v1||2…

A: Given that, Suppose v1 is a vector of all entries 1 in ℝn space, which we call 1-vector. What is…

Q: find the distance d(u, v) between u and v in the given exercise.

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Q: (c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)

A: Given: The coordinate transformation, x=Rsinhχsinθcosϕ y=Rsinhχsinθsinϕ z=Rcoshχcosθ The plane…

Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: Consider the set of vectors S = {2 – x + 4x², 3 + 6x + 2x², 2 + 10x – 4x²} in P2. Show that the set…

A: use linear independent vector definition

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: -91 Let y = -3 and u = and 2 orthogonal to u. x₁ = 4 -2 Write y as the sum of two orthogonal…

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Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: Find the point on the graph of z: (x2 + + 4y") at which vector n = - P =

A: Given,  (a)   z=-x2+4y2,   n=8,-80, 2  (b) f(x, y)=ex2+2y at (0, 0)

Q: (G) G)- The projection of onto the line through zero 1 is and а. (;) () " () b. C. d.

A: Let u→=11, and the line l through zero v→=00, and w→=1-1. Need to find the projection of u→ onto the…

Q: Let E The orthogonal projection of y on H = span{ u 1, ú 2} is given by:

A: Given

Q: 3 Compute the projection of i on ū = 1 proj, v =

A: The given vectors,v→=30-3  ,  u→=31-1

Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: Let x = (1, 1, 1, 1)T and y = (8, 2, 2, 0)T . Verify that x − p is orthogonal to p.

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Q: Consider the following. (4,-1, 0) 7, 0) Find u x V. Determine if uxV Is orthogonal to both u and v…

A: We have given  u=⟨4,-1,0⟩v=⟨-4,7,0⟩ Then, u×v=ijk4-10-470=i0-0-j0-0+k28-4=24k

Q: Find the orthogonal projection of y onto u 16 8. 48 OA. 32 4 OB. OC. OD. 32 - 16

A: We have to find orthogonal projection of y onto u

Q: Which of the followings is the vector projection of u onto v where u = -2i + 4j – V5k and v = 2i –…

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Q: Is v = |1a vector in the span of S = }|2| Use Gaussian elimination to support your answer.

A: To check v=111 a vector in a span of S=123, 012, -201 or not.

Q: The orthogonal projection of y onto u is the same as the orthogonal projection of y onto cu whenever…

A: solution

Q: Consider the following. u = −7i - 2j - 4k, V = 4j + 4k (a) Find the projection of u onto v.

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Q: Find the orthogonal projection of y onto u. y = -3/5] - 4/5 /5 4/5 b) c) d) 2.

A: The formula to find the orthogonal projection of y onto u is: projuy=u→.y→u→2.u→ Here,…

Q: Find the orthogonal projection of y onto u. - 8 4 y = u: 6. 12 O A. 1 4 3 4 О В. 4 12 Ос. 16 48 O D.…

A: We have to find orthogonal projection of y on u.

Q: 1 Find the vector projection of u onto v. u= 3i- 5j ++ 2k v=7i+j- 2k

A: Please refer the attached image for complete solution.

Q: find the projection of v onto u.

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Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ax + by + c.

A: Condition for perpendicular is: m1m2=-1 Part A: Consider the vector v=ai+bj x component of vector =…

Q: 8) Find the cross product a x b and verify that it is orthogonal to both a and b. a = (1, 1, -1),…

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Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

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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: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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Q: d) Find the orthogonal projection of v = 1 into U+. (1)

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Q: The projection of v onto w is v=i+j+2k, and w=i+2j+2k 3 =(-i+j+2k) а. (i + 2j +2k) 5 -(i + 2j + 2k)…

A: Projection vector of a⇀ on the b→ is given by c→=a→·b→b→b^

Q: Use the Wronskian to determine if the function vectors 7,= x? + e* and 72= e²x are linearly…

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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: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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Q: (ii) Let W = span{ } v = and The orthogonal projection of v onto W is projw(v) = and the component…

A: Given : v=-43-7    and W=span{ -2-32 , -3-1-2 } Aim: to find (a) projw(v)      ,and   (b) perpw(v)

Q: Let S be the parallelogram determined by the vectors b, 8. and b2 = 2 Compute the area of the image…

A: Given that S be the parallelogram determined by the vectors   The area of the parallelogram S is…

Q: 5. For which value of x do the following vectors form a linearly dependent set in R x,

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Q: 3. Use the Wronskian to determine whether the functions f1 = e*, f2 = sinx and f3 = x³ are linearly…

A: The Wronskian approach helps to find whether the given functions are linearly dependent or not. If…

Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w?

A: x is orthogonal to v and w. Then their dot product is zero. That is, ⇒x·v=0  &  x·w=0

Q: Evaluate zdz from z=0 to z-4+3i along the curve C given by the line from z=0 to z=3i and then the…

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Q: The orthogonal projection of v = 10i on b = –3i + j is <

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Q: -2 Let u 3 and w = 1 For what value of h is w in the plane spanned by u and 7 v? h

A: h = -17

Q: b) Show that the following wo matricegane orthogonal tker A =-V3 -2VTO 3/T15 15 E/NTS

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Q: Find the orthogonal projection of v=2 onto W.

A: