Suppose that Tui, Tus As lineady independent (Here, TELLU, W)) Prove that vi, Vz is linearly independet,

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: onow that the v ectors 2 3 do not span R' by giving a vector not in their span.

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Q: Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

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Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: prove by vector method that diagonals of rectangle are equal in length and bisect each oth

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Q: Let ā = (1,2),b = (x,y) and = (1,-2) find the value of x and y such that a is %3D %3D %3D orthogonal…

A: Given that a is orthogonal to b So a·b=0also we have c·b=2

Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: Find projection of vector (0, 1, 0) into the line spanned by (0, 1,0) 0(-1,0, 2) 0(-1,3, 2) O (0, 3,…

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Use vectors to prove that a parallelogram is a rectangle if and only if its diagonals are equal in…

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Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: Use the definition of the cross product to prove that the cross product of two parallel vectors is…

A: The cross product of two parallel vectors is zero. This can be proved by two definitions of cross…

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: show that the pants AC1,1,4), B(2,2,2), c(o,l,5) and D(1,0,5) coplanear (in the are Same plane).

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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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: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: We will prove that  (u*v)*w=(u.w)v-(v.w)u u*v=ijkuxuyuzvxvyvz…

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: Suggest a "vector proof" of the fact that, inR2, two lines with slopes m1and m2 are perpendicular if…

A: Given: ℝ2 To Prove that : m1 m2=-1

Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Suppose di ,de,..do ore distinct real numbecs det Prove ė lineerle fade pendent ere vectors in…

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Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

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Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Calculate the cross product assuming that u × v =〈1, 1, 0〉, u × w = 〈0, 3, 1〉, v × w = 〈2, −1, 1〉 v…

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Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Use vectors to prove that the line connecting the midpoints of two sides of a triangle is parallel…

A: Let the arbitrary triangle has vertices A, B and C has three vectors AB, →AC →  and  BC → . Let M…

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

A: We have, L1: x=4-t, y=2t, z=2+t and L2: x=1+4t, y=3-8t, z=5-4t

Q: If x, y are two no vectors, then prove that |xty | || X lle y llq by = + // use Holder inequality.

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Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Use a directed line segment to represent the vector.v = (−2, −5)

A: Let the given vector : Here, -2 represents x-cordinate and -5 represents y-cordinate.

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

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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: Determine whether Hhe Lindependent. by inspection Vectors are linearly 6. -2 -3

A: A vector is given

Q: Use a directed line segment to represent the vector.u = (2, −4)

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Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: Pind all point on 2=8-3x°- 243 where ohe bonyent plane is orehogonal :2-36,リ=タ +&e, 2-5-ビ to the…

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Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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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…