Let W be the orthogonal projection of U(4, -2, 7) on a(9, 2, 1). W = x a find x Answer:

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: Q2: (a) Find the scalar and vector projection of ū along ủ, where u¯=(2, 3, 4) and v¯=(2, 2, 0). (b)…

A: Given : u=2,3,4, v=2,2,0 we know that scalar projection of u along v is given by…

Q: Find the vector projection of onto v. u = 12i + 3jP + 4k U = i + j +k>

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Q: 2. Let x = (1, 1, 1, 1)" and y = (8, 2, 2, 0)". (a) Determine the angle 0 between x and y. (b) Find…

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Q: Consider the vectors u = (-2, 1, –3) and i = (1, –2, – 1). Find the angle between u and ū. (b) Find…

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Q: Consider the following. u = -7i - 4j - 2k, v = 4j + 4k (a) Find the projection of u onto v. -12 2k X…

A: Given :u=-7i-4j-2kv=4j+4k

Q: A linear transformation T: R → R? is given as 1 2 3 1 0 1 Y1 T: = Y2 Find all vectors 7 E R³ such…

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Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: a) Show that for a perpendicular projection matrix M, ΣΣμr(M). i j b) Prove that if M = M'M, then M…

A: According to the given information, For part (a) it is required to show that:

Q: Consider the following. = (3, 7), v = (4, 6) (a) Find the projection of u onto v. (b) Find the…

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Q: Let R be the parallelogram enclosed by the lines x + 3y = 0, x + 3y = 2, x + y = 1 and x + y = 4.…

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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: For each of the following pairs of vectors x and y,find the vector projection p of x onto y and…

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Q: The notation (x, y) (1.5x, 1.5y) defines a rotation in the coordinate plane. O True O False

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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: Let G(u, v) - (8u + v, 5u + 5v) be a map from the uv-plane to the xy-plane. Calculate Jac(G).

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Q: Find the orthogonal projection of u onto v.                                      u 1 2 3 v 2 -1 4

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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: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

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Q: Let u = 2i +j- 3k, v = i -j- k. %3D Find the vector projection Projuv o (2, 1, -3) O (1, 1, –3) O…

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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: O allet y be the orthogonal projection of y onto W. Then y depends on W and not on the

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Q: Find u × v and show that it is orthogonal to both u and v.u = (−1, 1, 2), v = (0, 1, −1)

A: Given vectors

Q: Find the orthogonal projection of y onto u. y = ,u = -3%5) b) c) d)

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Q: Consider the following. u = -9i - 2j - 4k, v = 4j + 4k (a) Find the projection of u onto v. -3j – 3k…

A: The given vectors,u=-9i-2j-4k, v=4j+4k

Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

Q: If F.T ds = 0, then F and T are orthogonal. %3D C O True False

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Q: . Calculate the projection of å along b and projection of b along å when: d = 3î + j – k , 5 = -21 –…

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Q: For each of the following pairs of vectors x and y,find the vector projection p of x onto y and…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = 2i + j…

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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: Let u= and w- Find the unique vector v in R'such that u.v 1, v is orthogonal to w, l|v|| V3, and y>…

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Q: In R°, let L be the line spanned and oriented by v = (2, –1, -4), and let R the rotation of IR…

A: Suppose L=αv:α∈R e line in R3R and R be rotation of R3 though angle π2 about v. Assume R:R3→R3…

Q: Suppose T: R³ → R² is a linear map and that u and v are particular vectors in R. If T(u) = (2, –3)…

A: Given query is to find the indicated vector.

Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = 3i − j…

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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) (i + 2j+ 2k) 3 (i…

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Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: Let p = (2, t) and q = (3,5). Find t such that p and q are orthogonal. (Give your answer in two…

A: We will use the property of orthogonality

Q: Find the orthogonal projection of y onto Span{u,, uz} 4 1 1 y =| 2 2 3 7 a. 6 5 3 44 b. 15 37 15 29…

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Q: Use a graphing utility to find u × v, and then show that it is orthogonal to both u and v.u = −2i +…

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Q: 3. Show your work. Simplify your results. -{()}-- () and b= Let L = Span (b) (c) Find the matrix P…

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Q: Consider the vector-valued function F(2,) = [xy² + 2ye* х, у y 3xe-y Which of the following are NOT…

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Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PQ and b= PR. Find %3D (c) The…

A: To obtain the vectors a=PQ→ and b=PR→, find the differences of the points P, Q and P, R,…

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

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Q: (d) If w E R" then the function fw : R" R defined by fw (v) =v•w for all v E R" is a linear form.…

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Q: For each of the following pairs of vectors x and y, find the vector projection p of x onto y and…

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

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Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

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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