e|| x°zdS, where S is the part of the plane z = 1+ 4x + 2y above the rectangle [0, 4] x [0, 2] Evaluate

Q: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

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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: Determine the point on the plane 4x- 2y + : = 1 that is closest to the point (-2,-1,5)

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to -1 √(-2¹ - 122³ - 30x²…

A: Since you have uploaded multiple questions, according to our guidelines we have solved first…

Q: Find the equation of the plane parallel to the intersecting lines (1,2 +t, -3 – 3t) and (1 – t, 2 –…

A: Let, the direction vector of 1,2+t,-3-3t is v1=0,1,-3 and the direction vector of 1-t,2-3t,-3-2t is…

Q: 2. (§1.1) Sketch the following set of points in the x-y plane. {(x, y) = R²: (y - x²) (y + x²) < 0}.

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Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Find the value of k so that the line [x, y, z] = [2, -2, 0] + t[3, 5, k] is parallel to the plane 4x…

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Q: find the point of intersection for the following 3 planes  x–2y+z+6=0 2x+y–z+2=0 2x+y+3z+2=0

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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Q: Find the point at which the line r(t) = (7, −7, 4) + t(−6, 6, −8) intersects the az plane.…

A: To find the point where the line intersects xz plane

Q: The line L(t) = (3+t, 12+5t, -12-5t) intersects the plane 5x - 5y = 15 at what point?

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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: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: Find the intersection of the plane x - X = y = - 4y - 5z = -137 and the line r(t) = (5, −5, −4)t +…

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Q: Sketch the set of points in the plane which satisfy the equation y + 2 = 3(x − 4)

A: We have to draw the graph for y+2=3(x-4)

Q: Consider the following diagram. The point O represents the origin of the zy-plane. The shape BCDE…

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