Let T: R'- R be defined by T(a, b, c) =(a + b, b– 2c, à + 2c). For cach vector B in R3 determine whether or not Be R(T). (a) B = (1, 3, –2) (b) B = (2, 1, 1)

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A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

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A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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A: The curl of a vector field F is defined as  ∇×F=i^j^k^∂∂x∂∂y∂∂zf1f2f3

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

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Q: Let, T:R' → R';T(x, y,z) = (x – y,2x + 3y + 2z,x+ y+2z) . verify that [T][v], = [T (v)]; for any…

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

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A: A=12541022011-4-9-21 ,b=12543-51The augmented matrix of the system is 12541022011-4-9-2112543-51now…

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