) Determine whether vectors v,(1,2,1), v2 = (1,0,2) and V3 = (1,1,0) spans the vector space (R³, R , +,.) or not? %3D %3D

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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: What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

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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) 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 orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

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Q: 3. Find the projection of u = (2,1,2) onto v = (0,3,4) and the vector component of u orthogonal to…

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Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

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Q: Determine all vectors v that are orthogonal to u.u = (2, −1, 1, 2)

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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: Consider the vectors [2, 1,0,0], [3, 1,0,0], [0,0,0, 1] in R'. Find a vector v so that v, [2, 1,0,…

A: We know four vectors v1 , v2 , v3 and v4 in ℝ4  will be linearly independent iff , av1→ + bv2→ +…

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: 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: Consider the points A(1, −1, 1) and B(3, 2, −1) in the three dimensional space. Find two unit…

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Q: 2. Consider the vectors [2, 1, 0, 0], [3, 1,0, 0], [0,0, 0, 1) in R". Find a vector v so that v, (2,…

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

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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: 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: Let u =(0,1,2) and v=(-2,2,0). Find %3D a. A vector w orthogonal to both u and v. b. The area of the…

A: The orthogonal vector both u and v is u×v . And the area of parallelogram is |u×v|

Q: Consider the vectors (2, 1,0, 0), [3, 1,0, 0], [0,0, 0, 1] in R". Find a vector v so that v,…

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Q: 19. Find two unit vectors perpendicular to vector u= (7, 0, -1) and vector v = (1, -1, 1).

A: We have to find the unit vector

Q: Find the length of the vector. v = (-2, 0, 5, 1) %3D ||| M = %3D

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Q: find the sum of vector AB and CD where A (1,-1) B (2,0) C(-,3) D(-2,2)

A: Let A (1,-1) B (2,0) C(-1,3) D(-2,2) be the given vector. Of course here in the problem   "-1"is…

Q: Find the vector component of the vector U orthogonal to a: и %3D (4, —1,2) and a %3D (1,3, —2).…

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Q: Find the scalar and vector projections of b onto a, where a = (-1, 1, 2) and b = (-2,7,2). 1. comp,…

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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: Describe the span ot the two vectors (1,0,9) and co. 1,15 geometricellyy in

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Q: Find the length of the vector.v = (2, 0, −5, 5)

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Q: Show that the vectors , and are coplanar.

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Q: Show that VI = (1,0,1) , v, = (1,1,0) , v3 = (1,1,1) span R'. Express vector v= (2, 1, 3) as linear…

A: v1 ,v2 ,v3 ,...,vn span R^n if det(v1,v2,...,vn) is non zero

Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: 2. Consider the vectors [2, 1,0, 0], [3, 1, 0, 0], [0, 0,0, 1)] in R'. Find a vector v so that v,…

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Q: 5. Find a nonzero vector orthogonal to the plane through the points P(1,0, 1), Q(-2, 1, 3), and R(4,…

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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: Find a vector that is orthogonal to the plane containing the points P = (3,0, 1), Q = (4, –2, 1) and…

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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 magnitude of vector AB. 1. A = (4, -3) and B 2. A = (-2, 11) and B = (2, 8) = (-8, 2) %3D…

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Q: determine projection of the vector b = -1 1 1 on the space generated by the vectors {--E)--[ -[+]}…

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Q: Find a vector ~v ∈ R^3 such that ~v is orthogonal to the vectors (2, 3, −1) and (1, −2, 3) and ~v ·…

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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: Use the vectors u= (3, 6), v=(-6,5) to find the indicated quantity. State whether the result is a…

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Q: Identify the vectors that are orthogonal to v = (1,2, 1) but not to w = (1,0, – 1). 口(-2,2,0) (-1,…

A: u and v orthogonal if u.v=0 i.e. let u=(x1,y1,z1) and v=(x2,y2,z2) then u.v = (x1 * x2)+(y1 *…

Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

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Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…