3. Find the vector component of u along a and the vector component of u orthogonal to a for the given vectors u = (2,0,1) and a = (1,2,3)

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩     (1/3)z − 3u = w

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Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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Q: Find a unit vector orthogonal to both u and v. u = 8i – 16j + 2k v = 16i + 32j – 6k -

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Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.

A: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.…

Q: a) for which values on are the vectors V3 = 2 %3D 7 19 linearly independent?

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Q: Please solve this linear algebra question. Thank you

A: According to the given information, It is required to show that u, v, w are linearly independent…

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: Find an equation of the plane that passes through the point P(4, 7, 1) and has the vector n = (1, 3,…

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Q: Let vi, ..., v be vectors, and suppose that a point mass of m,, ..., m, is located at the tip of…

A: Given: u1=-1, 0, 2   and     m1=2u2=2, 1, -3   and     m2=1u3=0, 4, 3       and     m3=4u4=5, 2, 0…

Q: Find a unit vector orthogonal to both u and v. u = 3i + 5j + 2k V= 위해 + -k 10

A: Given the vectors u→=3i→+5j→+2k→, v→=12i→-34j→+110k→. To find: A unit vector orthogonal to both u→…

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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Q: Determine all vectors v that are orthogonal to u.u = (0, −4, 3)

A: Given u=(0,-4, 3)we have to find all vectors v that are orthogonal to u,If u.v =0 then vectors u and…

Q: Determine if the given vectors are coplanar u = 2i - j - k; v = 4i + 3j + 2k; w = 6i + 7j + 5k

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Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

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A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Determine all vectors v that are orthogonal to u.u = (0, 1, 2, −1)

A:

Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

A:

Q: Find the magnitude of u xv and the unit vector u= 5i - 5i - 3k, v= 0 O A. 0; 5i - 5i - 3k O B. V59;…

A: Here we have, u=5i-5j-3k and v=0 We have to find the magnitude of u×v and the unit vector parallel…

Q: Find the projection of u onto v and find the vector component of u orthogonal to v. u = ⟨8, 2, 0⟩,…

A: Consider the given vector u=8,2,0 and v=2,1,-1

Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: 1. Consider the vectors a = (1, 1, 1) and y = (1, 1, 3) in Rº. Compute æ x y. 2. Show that, for æ, y…

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Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

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Q: Find a unit vector orthogonal to both u and v. u = 3i + 5j + 2k 1 + -k % = 2 4 10

A: We have to find the vector

Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: Suppose u, v, w are linearly independent vectors. Prove that S is linearly independent where (a) S=…

A: A set of vectors v1 , v2 , v3 ,...,vk from a vector space V  is said to be linearly independent , if…

Q: Find the coordinate vector of w relative to the basis S= = (u1, u2) for R. Let u = (2, –3), u2 = (3,…

A: Given

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

A: Given that                   y→=-4-3 and u→=66.

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: Let u = (-1,0,1), v= (3,2, 1) and w = (0,1, 2) . (a) Prove that the vectors u – v, u+ v and u x v…

A: Given : u=<-1,0,1> v=<3,2,1> w=<0,1,2>

Q: for any R value of the third, so that the following vectors are linearly related and loudspeaker…

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Q: Find the vector z, given that u = (3, 2, 9), v = (2, 2, -1), and w = (4, 0, -4). %3= z = u - v + 2w

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Q: 2. Let i= and (a) Compute the length of the vector u.

A:

Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: Determine all vectors v that are orthogonal to u.u = (0, 5)

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Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: Find the vector projection of vector u onto vector v, and find the vector component of u orthogonal…

A: The projection of vector u onto v is given by projvu=u⇀v⇀v⇀2v⇀

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: Linear algebra

A: From the given information:Let,

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

A:

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector