Let ū = (2, –4), ū = (0, –5), and w = (-5, –3). Find the vector x that satisfies %3D би — о +х — бх + w. In this case, x =

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

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Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

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Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: 2. Choose the linearly dependent vectors in R

A: two non zero vectors V1, V2 are said to be linearly independent if and only if aV1+bV2= 0 ⇒ a=0 and…

Q: * Find the values for h for which the vectors are linearly dependent: 7

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

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

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Q: Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5,…

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Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a…

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Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = <1, 2, 3> v = <2, 2, -1> w = <4, 0, -4>

Q: A vector u for which || u || = 1 is called a(n)_______ vector.

A: u is a vector whose modulus is 1. u=1 For a vector, if the modulus or magnitude is 1 then the vector…

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector - [';" - a 1 - ] a P = b

A: From the given information, P=1-aab1-b Let, stable vector as, w=xy

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: Г 13 and vz = 14 are linearly independent. Determine whether the vectors v 14

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Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

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Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: Find vector c = 3u – v, if u = and v =.

A: Given u = 2i - 7j + 3k and             v = 0i + 4j -  k = 4j - k Now vector c = 3u - (1/2)v c = 3(2i…

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Suppose v1, ..., vn are linearly independent and Span({v1, .., vn}) = V , then if W ⊂ V and W…

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Q: At what value of k are these vectors collinear?

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Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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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 three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=&lt;1,1,1&gt; The second case we can take b=&lt;0,1,-1&gt; The…

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: If ï = (, 2), find a vector i that is perpendicular to ū.

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

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Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=&lt;2,-2,1&gt;.

Q: Determine R21, the vector from P2(5,2,–4) to P1 (3,–1,0). 2аx + Зау — 4а, —2ах — Зау + 4az 4ax + ay…

A: Consider the following vectors: P→1=3ax-ayP→2=5ax+2ay-4az…

Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

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: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

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Q: Let u and v = .A vector orthogonal to both ú and v is

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Q: The vector 1 is in Span{ V2, ., Vm } if and only if ( V1..., Vm ) are linearly dependent. O True…

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Q: Find the given vector. Vector v of length 4 in the direction of = (-4, -4)

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Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

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Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

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