x-z+4 8x-y+3z² 3. Given vectors field G = 3* 4+z2 :ax + y3+z - ay and a position vector, r, = 2ax – 3ay + %3D 2x4 4az, determine: (a) G(rp) (b) Unit vector in the direction of vector field G at point P.

Q: = (4, 1, a), Q = (–2, 0, b) and v = i – 3j + 4k be two points and a vector in R³ respectively. (a)…

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Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Let S be a linear transformation from R³ to R2 with associated matrix Let T be a linear…

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Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: A = 4i - 2j+4k and B = 3i – 6j – 2k, be two non-zero vectors. Find i. A.B. ii. the angle between A…

A: According the guidelines we solve only first one question with all subpart.

Q: 4 В T(t+h) A 21 y 01 2

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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: 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: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

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Q: Calculate the triple scalar products w. (vx u) and u (w x v), where u = (7, 2, -1), v = (2, 8, -3),…

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Q: Find Vz. 3ce3y x + 8y NOTE: Give your answer in unit vector notation; that is, in terms of i and j.…

A: given  z=3xe3yx+8y   and we know  ∇z=∂z∂xi→+∂z∂yj→…

Q: Q4) The vector product of two vectors is scalar product. F O T

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Q: Find the matrix of the linear transformation that sends a vector to its reflection to the plane x1 –…

A: To find : matrix of the linear transformation that sends a vector to its reflection to the plane…

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

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Q: Suppose that u and v are orthogonal vectors in R’ of lengths 1 and 2, respectively, and suppose that…

A: Answer

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Suppose a, b, c are vectors in R³ for which Then (22a) ((14b) x (10c)) = Check det[a b c] = 2 Which…

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Q: Consider the two bases B = {b₁,b2} and C = {₁, 2} for R² where 3 5 = = - [B]-4-[13] 4-[8]), 4-[8] =…

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Q: (2) Let vị = ( 2 = (2),v3 1 of the vector space R³. (2a) Does the vector v = (6 belong to…

A: Linearly independent vectors: The set of vectors v1, v2, ..., vn is said to be linearly independent…

Q: Given vectors (A = a₁ + a₂) and (B = 2a,- 2ay - a₂), when A is defined by Q (1,1,1) find (i) AXB…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…