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

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Find a unit vector orthogonal to both u = (1, -2, 1) v =(2, 1, 0)

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Q: Can the vector (3, −5, 2) ∈ R3 be written as a linear combination of the vectors v1 = (2, −3, 1) v2…

A: Linear Combination:Let V be a vector space and S = {v1, v2, · · · vn} ⊆ V . Then for α1, α2, · · ·…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

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Q: photo attached

A: Given point can be written in vector form as,

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: A three-dimensional unit vector parallel to the y-axis is

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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: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

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

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Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

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

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Q: Two linearly independent vectors in R3 span R2, is that true

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

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: What is the vector translating A to B? B to A? What is the effect of a translation?

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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: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

Q: 2 nogonal to the vector

A: The coordinates of point M is 1,1,0 . The orthogonal vector to M is 200. The equation of the plane…

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

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

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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 a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: Consider the vector v = ⟨v1, v2, v3⟩. What is the meaning of arccos v2 / II v II = 30°?

A: Consider the vector v=v1,v2,v3 Use the dot product rule: v·j=v×jcosθ=vcosθ where θ is the angle…

Q: Find the unit vector in the same direction as the vector u = [-8, 6, 7].

A: Given,         The unit vector in the same direction as the vector u=-8,6,7.

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

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: Find a unit vector that is orthogonal to both u and = (-8, -6, 4) v = (17, -18, -1)

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

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Q: Find a unit vector u in the direction opposite of (-8,-4,-3).

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Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

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Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

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: Find the vector with length V17 and same direction as i= (7,0, –6).

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Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

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Q: Find a unit vector which is perpendicular to both đ = (1, 1, 0) and b = (-2, 3, 0) Answer:

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

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: Find the magnitude of the resultant vector. (-25.6, 7.7)- (-11, -9.8) 1R

A: letA→=-25.6, 7.7 and B→=-11,-9.8

Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

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 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: Find a unit vector u that had the same directions as the vector v= (-3,3,-2)

A: Use the basic property of unit vector

Q: Describe a unit vector in R^3 with the same direction as <1,0,7>

A: Consider the given point vector

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

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