/ If A(1,23=1), B(3)6-7), C(233,-3),D(34-3), Cal culate the angle between the vector Projection of ÁB onto Ac and the vector Perpendical ar on Plane determined by BC a nd Dc

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Find the projection of vector ū = -i+ 5j + 3k onto the vector i = -i +j- 3k? %3D

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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

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Q: Find a unit vector perpendicular to both u = (2,3, –4) and v = (-1,1,–4). %3D

A: The unit vector perpendicular to u and v is given by: w=±(u×v)|u×v|

Q: Find two unit vectors orthogonal to both u = (1, 2, – 3) and = (0, 1, 2). %3D unit vectors =

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: Determine the resulting vector when á = (-2,4) is rotated 60° clockwise and increased in size %3D by…

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Q: In a 4-D Euclidean plane, vectoru = (a, b, c, d). In a 3-D space, vector v = (2,7,c). What is u + v?…

A: Given :  Vector u = <a, b, c, d>  Vector v = <2, 7, c>     To find the vector u + v.

Q: Calculate parallel component of vector a = [1,2.2] in the directoin of vector v = [7,7, 7].

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: Let vector u= 3,4 and vector v= 6,7. Find the magnitude of 3u-4v

A: The vectors are given by u = 3,4 v = 6,7 To evaluate : The magnitude of 3u-4v

Q: Find the projection of vector A=(6,7) along vector B=(1,4).

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: we have to represent the line segment from P to Q by a vector valued function and by a set of…

Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

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Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: 1. Express A = (3, 1, –1) as B+ C, where B is parallel to the vector (1, 4, 2) and C is…

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Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Describe all vectors v that are orthogonal to u

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Calculate the coordinates of the vector w obtained by rotating anticlockwise the vector v= [0, -1,…

A: When a coordinate is being rotated along the direction of a vector by a certain angle, the new…

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: Determine the vector projection of the vector (5,0, 7) on the vector (–1,3,4).

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Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

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Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Find the magnitude of the projection of (- 5, – 5) onto the vector (- 2, – 7) Round your answer to…

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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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: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Given information: The points are P(0, 0, 0), Q(5, 2, 2). Calculation: Find the vector valued…