Use a software program or a graphing utility with vector capabilities to find the lengths of u and v, a unit vector in the direction of v, a unit vector in the direction opposite that of u, u· v, u.u, and v v. (Round your answers to four decimal places.) , 1, v3), v-(-1, v3, -1) (a) |u| - ||v|| = the norms of u and v (b) a unit vector in the direction of v (c) a unit vector in the direction opposite that of u (d) u'V (e) n.n (f) v.v

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find a unit vector orthogonal to both u and v. (-3, 4, –2) (-1, 1, 0) u = V = 2 2 1 3' 3' 3

A: Given two vectors u and v, then the vector that is orthogonal to both u and v is their cross…

Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: Find a unit vector that is orthogonal to both u and v. u  =   −8, −6, 4   v  =   10, −18, −2

A: Given Vectors,u=⟨−8,−6,4⟩V=⟨10,−18,−2⟩We have fo find unit vector that isorthogonal fo both u and vA…

Q: Use vectors to determine whether the points are collinear (0, -2, -5), (12, 7, 1), (8, 4, –1) The…

A: Given: (0,-2,-5) , (12,7,1) & (8,4,-1) are three points.   To Check : The given points are…

Q: (c) Are the vectors = (3, 1, 2, 1), v2 = (-1,0,1,0), 03 independent? Explain why. (3,0,0,3), v4 (5,…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Use the graph to find the projection of u onto v. (The terminal points of the vectors in standard…

A: The given vectors are,u=(-1,2) and v=(4,2)

Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: If u,v and w are linearly independent vectors other than zero vector, are the vectors u, v ,…

A: No, Not Necessarily.

Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

Q: Exercise 5. Suppose v is a nonzero vector. Show that any vector w can be written as w = av+ u where…

A: This is a problem of vector space, vector algebra.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector that is orthogonal to both u = (- 1, 4, – 5) and v = (0,4,–7). %3D

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Q: Indicate the options that contain an orthogonal set of vectors:

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Q: 2. Determine whether the set of the vectors {V1, V2, V3, V4} are linearly dependent or independent.…

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Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given :           The vectors are 111 , 123 , 1-12   To determine the vectors are linearly…

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Find the distance from the point P(-3, 1,4) to the line through A(1, 1, 0) and B(-2, 3,-4).

Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: We have to use the method such that to find the distance from the point P(-3, 1,7) to the line…

Q: Define the vectors u = и %3 (-5, 2, –1) v = (3, 2, –5) - а)Compute u: 0. b)Is the angle between u…

A:

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: Note: I have solved this above proof by two vector method but is not correct point for…

Q: Determine if the vectors vị = (1,2, 3), v2 = (1,-1,–3), v3 = (1, 1, 1) span R³.

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Distance = 4.41

Q: Determine which of the vectors is (are) parallel to z. Use a graphing utility to confirm your…

A:

Q: Use the vectors u = (4, 4), v = (-6, 3), and w = (4, -1) to find the indicated quantity. (u v) - (u…

A: We have to find the indicated quantity. This problem can be solved using the dot product of the…

Q: Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Solution:

Q: Determine if the sets of vectors in Exercise are linearly independent. If for any of these, the…

A: Given: vectors 012, 213, 201   To find: If the given set of vectors are linearly independent or…

Q: 9. Find a unit vector perpendicular to both [1,2,-3] and [2, -1, 4].

A: Given a=i+2j-3k b=2i-j+4k Aim : to find unit vector perpendicular to a and b

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

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Q: 5. If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

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

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Q: The vertices of a triangle in space are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Explain how to…

A: Given:

Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: We need to find distance.

Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

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Q: (c) Are the vectors v1 = (3,1,2, 1), i2 = (-1,0,1,0), iz = (3,0,0,3), T4 = (5, –2,0, 4) linearly…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: A force is given by a vector F = (1,2, 3) and moves a particle from the point P(2, 1, 0) to the…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.