Consider the vectc 5, as shown in the Write the vector in , where a and b ar places.

Q: Find the unit vector in the direction of v and verify that it has length 1.

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Q: Find a unit vector e, where v = (1, 2, 3). ev

A: Unit vector is a vector that has magnitude 1 For a vector v=<x, y, z>Norm of vector v is…

Q: Find the following vector.   The vector in the direction of (24,10) with length 4

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Q: Find the unit vector in the direction of v and verify that it has length. v = ⟨−6.2, 3.4⟩

A: Now magnitude is,

Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

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Q: Find a vector v such that ||v|| = 20 and v is in the same direction as 15i + 15j

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Q: Draw the vector to show: (а) (b) (c)

A: A→ = AxAy , This is the representation of vector in matrix form. These type of matrices are called…

Q: Show that, û . ûm = 0, Use only the fact that û,is a unit vector. Interpret this result.

A: Here we need to prove that dot product of a unit vector and its derivative is zero. Here we use the…

Q: Represent the vector with respect to each of the two bases { ] y = B = B2 =

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Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: express each vector as a product of its length anddirection. 2i + j - 2k

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Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: Let å = . Find a unit vector in the direction of å

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Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: Find a vector v such that ||v||=20 and v is in the same direction as 15i+15j.

A: The parallel vector of a vector is the scalar multiple of the vector, and if scalar is positive then…

Q: Suppose that the vectors below have the following components: a = b= č = What is the exact value of

A: We have to find the exact value of the given vector multiplication.

Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Sketch the following vectors, and find their components andlengths: i + j + k

A: The vector is i+j+k sketch the vector and find its length.

Q: Express the vector in the form (a, b). 1(i + j) ji + jl

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Q: Let ā= . Find a unit vector in the direction of a

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Q: Find a vector that is oppositely directed to v = with a length of 4

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Q: Use the given vectors to compute u + v, u − v, and 5u − 3v. u = (5, −2),    v = (7, 6)

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Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Write w as the sum of a vector in Span{v} and a vector orthogonal to

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Q: Find the vector of length v7 in the direction of AB + AC

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Q: Find the following vector. The vector in the direction of (24,10) with length 2

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Q: Find a unit vector that has the same direction as the vector 87 – j + 4k.

A: Find a unit vector that has same direction as the vector 8i- j+ k.

Q: Find the unit vector in the directions of v, where Ans = %3D

A: To find unit vector in the direction of v, divide it by the length of v.

Q: B

A: Given that the diagram  Draw the vector C→ such that A→+B→+C→=0.

Q: Find a unit vector that has the same direction as  4i − j + 8k.

A: we have to find a unit vector that has the same direction as 4i-j+8k let the given vector be a→…

Q: Find the following for the vectors

A: Given that: v=-9i+ju=-5i+7j     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Find the unit vector of u=.

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Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: Given P-4,1, Q3,-4, R2,6 To find the unit vector with the same direction as QR→

Q: 3 Compute the length of the vector v =

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Q: Express the following vector as a product of its length and direction: v = 4i + 8j – 16k -

A: Given vector is v→=4i+8j−16k. We have to express the given vector as a product of its length and…

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

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Q: Find the unit vector in the direction of the given vector a, and express it using standard unit…

A: Find the unit vector in the direction of the given vector a . vector a = 20i - 21j  . Here i…

Q: Let å = . Find a unit vector in the direction of a

A: Givena→=⟨4,−3,−4⟩

Q: Write the unit vector v in compa sketch. a) Ivl = 8,0 = 45

A: a)v=8, θ=45

Q: Find a unit vector that is orthogonal to both ı̂ +ȷ̂  and ı̂ +?̂

A: Given query is to find the unit orthogonal vector to the given vectors.

Q: Find a vector that is oppositely directed to v = with a length of V3

A: We have to find the vector by given data

Q: Find the length of the vector T

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Q: Find the magnitude of the following vector. (-1, 2)

A: Given<-1 , 2>

Q: Let ā = . Find a unit vector in the direction of a

A: For any vector a→, the unit vector in the direction of  a→ is a→a.

Q: Find a unit vector e, where v = (4,9, 4). ev

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Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: It is known that the unit vector along the direction v is given by vv. Since it is an unit vector,…

Q: Find a nonzero column vector u such that Cu = 4u.

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Q: Assuming vector B is 12 units long, vector 4B is:

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.