4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are symmetric.

Q: Calculate the component of v = 〈− 2, 1/2 , 3〉along w =〈1, 2, 2〉.

A: Given: Vector, v=-2,12,3 Vector, w=1,2,2

Q: True or false? If v is a direction vector for a line L, then −v is alsoa direction vector for L.

A: True or false. If v is a direction vector for a line L, then -v is also a direction vector for L.

Q: 1. Consider the pointsS= (1,−3) andT= (2,5).(a) Sketch the vector−→ST.(b) Give the component form…

A: Here 2 different problems are provided. As per our Bartleby Guidelines, we are supposed to…

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Let T: R² → R² be a reflection in the x-axis. Find the image of each vector. (a) (2,7) (b) (6, -8)…

A: T: R2 - >  R2 is a inear map which is basically reflection in the x Axis. Therefore for any point…

Q: (2) For every vector u and vector v in se A) True B False

A: Introduction: Vector is a quantity that has both magnitude and direction. Some mathematical…

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Q3) A) Let 4 (-1 3, 4) and B (-5, 8, 10) two points in the space, find: 1- The vector AB. 2- Length…

A:

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

A:

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

A:

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

Q: 16. Let F = 2a, - 6a, = 10a- and G = a, + G,a, + 5a;. If F and G have the same unit vector, G, is…

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: -3 3 Let u = -5 and i: 7 Find a vector w not in span {u, v}. 4 -3

A:

Q: Let <··· Give the B-coordinate vector for each of the following: (a) B = H ²21 (b) 2 (c) H

A:

Q: Does A(u x v) = Auxv +ux Av?

A:

Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

A:

Q: Let T: R2 R be a reflection in the line y = x. Find the image of each vector. (a) (0, 8) (b) (1,-1)…

A: Let T:R2→R2 be a reflection in the line y=x.

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

A:

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

A:

Q: CHCR) and C= Let B= - 3 of vis [v]B 1 1 [;)] 3 = A [v] 0 M-[2] 3 ⓇM1.- [³] B [v] = 0 0 4-A] -9 Ⓒ…

A:

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: Set a = 0 gives Uo = {(x1,x2, x3)T E R³|x1 + 2x2 = 0}. Define an operation O for the vectors in R3…

A:

Q: If a = (4, 0, -1), find a vector b such that comp₂b = 3. b = X

A: a=&lt;4,0,-1&gt;ab=3ab=a→.b→a→let b=&lt;b1,b2,b3&gt;

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: Let a, b, and c be vectors. Is it a vector, scalar, or is in meaningless? 1) ( a X b ) + a.b 2) -2 +…

A: We will whether the part 1, 2 and 3 are a vector or a scalar or meaningless as following.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.