Let the contour C be the triangle with vertices (0,0), (2, 0), and (0, 2), oriented counterclockwise. Let f(x + y) = xy + i(x² - 2y). Determine Sc f(z) dz.

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

A:

Q: Find Duf at P. f(x, y, z) = 6x³y³z³; P(2, — 2, 2); u = Duf = i + - 2|3 k

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Q: If the xy-coordinate axes are rotated , find the XY-coordinates of the point (x,y) = (4,5

A: The new coordinates (X, Y) of a point (x, y) can be found using the following rotation…

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: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.

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: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Let ä(t) = (5, 4, 2)t + (-6, -4,1) and (u) = (-2, 1, 2)u+ (2, -8,-6). Find the acute angle between…

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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.