1/2 |-1/4,v = 2] u -1/2] 2.

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v=ai+bj, where a and b…

A: Given ,  The vector v with initial point (0, 0) We have to write v in the form v = a i + b j where…

Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

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Q: Find a parametrization of the line passing through (2, 0, 4) and (4, 1, 2). r(t) =

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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: (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: Find the projection of u along v. u = 5i + 7j − 4k, v = k

A: Given, u = 5i + 7j − 4k, v = k To find the projection of u along v.

Q: The vector E %3D —а, — 4аф + За, еxpressed in RCS and in terms of ф is E 3 (-сosф + 4sinф)ax +…

A: This question is based on unit vector conversion from Cartesian to cylindrical system.

Q: A. If x and y are orthonormal vectors, then find the valne of x+ yl? - |x-yl

A:

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

A:

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v = ai+bj, where a and b…

A: It is given that initial point of vector v is (0,0). The objective is to write vector v in the form…

Q: For all u and v in R" with u + 0, show that u is orthogonal to v – u•v

A:

Q: 1. Let u= (0, -2,3), v= (1,4, 1). Evaluate a) the projection proju(v) of v over u And b) the area of…

A: Given: Let u= (0,-2,3)   and  v=(1,4,1) To find a) the proju(v)  of u over v b) area of the…

Q: nd the orthogonal trajectories of the family of confocal central conics given as: = 1 a² + à b² + à

A:

Q: Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их

A: Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Q: find all the scalars k such that || kv || = 3, Where v = (-1, 2, 0, 3)

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

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

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

A:

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 –…

A:

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

A: Cross product is,

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: Show that the functions o,(x) = sin(nax²), for n = 1,2,3,..., form are orthogonal set with respect…

A: Consider the equation

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…

A:

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

A: We need to find the distance between the two vectors.

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 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 u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)

A: We have given; u = (1, 1, 0), v = (0, 3, 0)

Q: Consider the following. u = (-2, 2), v = (1, 1) %3D %3D (a) Find u v.

A: Given two vectors:

Q: Compute the component of u along v. u =〈3, 2, 1〉 v =〈1, 0, 1〉

A: Given the vectors are u=<3,2,1> and <1,0,1>.Our Aim is to compute the component of u…

Q: Find the distance between u and v.u = (1, −1), v = (−1, 1)

A:

Q: Calculate the projection of f = 4 i - j +7k on g = 3 i +2j – 6 k

A: Projection in vector:       The vector projection of a vector a on (or onto) a nonzero vector b…

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) =

A:

Q: Find a lower triangular L and an upper triangular U so that A = LU. %3D 1 2 0 1 2 4 1 4 A = %3D 3 6…

A: Given: A=120124143639 To compute L & U

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

A:

Q: Find the projection of u onto v, proj,u, given u = and v = .

A: PFA

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: Use the given transformation to evaluate the integral. (12x + 12y) dA, where R is the parallelogram…

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Q: Consider the following. u--8i-4j-2k, v - 4j+4k (a) Find the projection of u onto v. (b) Find the…

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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: |The vector projection of v = 4î + 4j + 4k onto W = 5î - 4ĵ + 3k is aî + bî +cê: where the exact…

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Q: 2. Show that the ry plane W = (r, y, 0) in R³ is generated by: (i)u = |2 and v= (ii)u = and v=

A: Please see the below picture for detailed solution.

Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: onto y %3D Find the projection of I =

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

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Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…

Q: (f) Find the length of the projection of i onto ū.

A: Given