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

Q: Prove that if u is the vector function with the constant value C, then du/dt = 0.

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

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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: The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and…

A: Given that m=6,n=8to find the chiral vector of SWNT.  As we know that, the chiral vector c can be…

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

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

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: 18 as a linear combination of a and y Express the vector v y.

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Q: Q2) A- Use two methods to create the vector x having 100 regularly spaced values starting at 5 and…

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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: Let F = 3 x R, where is a constant vector. Calculate F. dR C on the line segment C connecting (1, 3,…

A: According to the given information, it is required to calculate the integral.

Q: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

Q: 2) If A =,find grad(div A), where r is a position vector.

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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: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: Query- Give an example of a linear combination that resulted in the zero vector that did NOT have…

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

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Q: () - Does vector T = belong to Span (S), where

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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: 3 Compute the length of the vector v =

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Q: Le and ü .Write j as the sum of two orthogonal vectors, a, in Span {u} and i2 orthogonal to ū.

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Q: State the difference between a position veetor and a line vector.

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Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

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

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

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

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Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: In what direction should one move from the point (2, 3) to increase 4x?y most rapidly? Present your…

A: The solution is given below

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: 2. Prove the following identities related to the cross product of vectors (а) (и х у)хw — (u · w)v –…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Prove that the vector T'(t) = 0 for moving in a straight line

A: Note that, the object's path is rt=xti+ytj. yt=mxt+b, where m and b are constant. It is known that,…

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

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: Let T R2 R2 be a linear transfor [3] into the vector a (i) T maps vector u

A: Introduction: A linear transformation could be a operation from one vector area to a different one…

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

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

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Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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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 a vector x whose image under T,

A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

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: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

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