Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces. (0,0,0) to find the flux of F through the The square with corners (1, 1, 1), (1, −1, 1), (−1, 1, 1), and (-1, -1, 1), oriented upward. Hint: Use the fact that this is a face of a cube centered at the origin.

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: Transform the equation: 2x2y'' + xy' + 3y = 0 to the form of: a(d2y/dz2) + b(dy/dz) + cy = 0 (a,…

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Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: Find the scalar equation for the plane passing through the point P=(−5, 3, 2) and containing the…

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Q: What kind of transformation results in applying the rule (x, y) → (x – 5, y) in the coordinate…

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Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3…

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Calculate the cross product assuming that u x w = (6, 3, 6) (-u+3w) x w =

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Q: Find the intersection of the line that passes through (0,3,-1), in the direction of…

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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: ind the point of intersection for the lines v(t) = (-5, - 8, -6)t + (− 1, 3, 1) and (u) = (6, 6, 2)u…

A: First we find value of parameters u and t .

Q: Find ((x2 + 4y)i + 3 y j) · dř where C consists of the three line segments from (1,0,0) to (1,4, 0)…

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Q: c that make the convolution equal to zero for the vector function F(x, y, z) = (2az + y – 5x)i + (2x…

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