Use Stokes's Theorem to evaluate EF. dr. In this case, C is oriented counterclockwise as viewed from above. F(x, y, z) = 2yi + 3zj + xk C: triangle with vertices (9, 0, 0), (0, 9, 0), (0, 0, 9)

Q: u = (15,0, 7) and v = (3, 8, 5). The cross product u x v is equal to:

A: Given vectors are

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Find the cross product u x v where i = 3i +6j +9k and v = (- 2, – 4, 5). ux v =

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Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Use Green's Theorem to evaluate (V1+r) dr+2ry dy, where C is the triangle with vertices (0, 0),…

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Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Find the circulation f V. dR, where V = yi + (x² + y²)j + (x + y)k, and C' is the triangle with…

A: In this question we will find the circulation of

Q: Find the cosine of the angle between the planes -3x - 4y – 3z = 3 and the plane - 1x - 3y + 3z = -2.

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Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

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: Let v = (3, 0, 0) and w = (0, 1, −1). Determine u = v × w usingthe geometric properties of the cross…

A: Cross product: more formally called the vector product a way of multiplying two vectors and produces…

Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Q: Use Green's theorem to evaluate F.dr where F(x, y) = xy² i+ (1 – xy³) j and C is the parallelogram…

A: Using Green theorem the integral becomes:  ∫Cxy2dx+1-xy3dy=∬S∂∂x1-xy3-∂∂yxy2dxdy where S is the…

Q: 3x, - 2x, + 4x, = 1 X, + X2 - 2x, = 3 2x, - 3x, + 6x, = 8 %D Select one: a. no solution b.…

A: The given system of equations,3x1-2x2+4x3=1x1+x2-2x3=32x1-3x2+6x3=8

Q: Use Green's Theorem to evaluate $. xydx + x²y³dy, where C is the triangle with vertices (0,0), (1,0)…

A: Consider the provided question, ∮cxydx+x2y3dy,     where c is the triangle with vertices 0,0, 1,0…

Q: Evaluate ſc zsin(2²) dz where C is the union of the lower-half of the unit circe in clockwise…

A: The complete solutions are given below

Q: Find the cross product a x b. a = (2, 5, 0), b = (1, 0, 3) Verify that it is orthogonal to both a…

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Q: Let the contour C be the triangle with vertices (0,0), (2, 0), and (0, 2), oriented…

A: In this question, we will find the integral.

Q: The endpoints of AB are A(4,3) and B (1,1). What are the coordinates of A" after the image has been…

A: Coordinates of A.